Question. 1

Vimla starts for office every day at 9 am and reaches exactly on time if she drives at her usual speed of 40 km/hr. She is late by 6 minutes if she drives at 35 km/hr. One day, she covers two-thirds of her distance to office in one-thirds of her usual time to reach office, and then stops for 8 minutes. The speed, in km/hr, at which she should drive the remaining distance to reach office exactly on time is

(a) (b) (c) (d)
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Question. 2

A and B are two railway stations 90 km apart. A train leaves A at 9:00 am, heading towards B at a speed of 40 km/hr. Another train leaves B at 10:30 am, heading towards A at a speed of 20 km/hr. The trains meet each other at

(a) (b) (c) (d)
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Question. 3

Anil, Sunil, and Ravi run along a circular path of length 3 km, starting from the same point at the same time, and going in the clockwise direction. If they run at speeds of 15 km/hr, 10 km/hr, and 8 km/hr, respectively, how much distance in km will Ravi have run when Anil and Sunil meet again for the first time at the starting point?

(a) (b) (c) (d)
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Question. 4

A contractor agreed to construct a 6 km road in 200 days. He employed 140 persons for the work. After 60 days, he realized that only 1.5 km road has been completed. How many additional people would he need to employ in order to finish the work exactly on time?

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Question. 5

John takes twice as much time as Jack to finish a job. Jack and Jim together take one-thirds of the time to finish the job than John takes working alone. Moreover, in order to finish the job, John takes three days more than that taken by three of them working together. In how many days will Jim finish the job working alone?

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Question. 6

A and B are two points on a straight line. Ram runs from A to B while Rahim runs from B to A. After crossing each other, Ram and Rahim reach their destinations in one minutes and four minutes, respectively. If they start at the same time, then the ratio of Ram's speed to Rahim's speed is

(a) (b) (c) (d)
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Question. 7

Two circular tracks T1 and T2 of radii 100 m and 20 m, respectively touch at a point A. Starting from A at the same time, Ram and Rahim are walking on track T1 and track T2 at speeds 15 km/hr and 5 km/hr respectively. The number of full rounds that Ram will make before he meets Rahim again for the first time is

(a) (b) (c) (d)
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Question. 8

The distance from B to C is thrice that from A to B. Two trains travel from A to C via B. The speed of train 2 is double that of train 1 while traveling from A to B and their speeds are interchanged while traveling from B to C. The ratio of the time taken by train 1 to that taken by train 2 in travelling from A to C is

(a) (b) (c) (d)
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Question. 9

In a car race, car A beats car B by 45 km, car B beats car C by 50 km, and car A beats car C by 90 km. The distance (in km) over which the race has been conducted is

(a) (b) (c) (d)
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Question. 10

Leaving home at the same time, Amal reaches office at 10:15 am if he travels at 8kmph, and at 9:40 am if he travels at 15kmph. Leaving home at 9:10 am, at what speed, in kmph, must he travel so as to reach office exactly at 10:00 am?

(a) (b) (c) (d)
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Question. 11

Two persons are walking beside a railway track at respective speeds of 2 and 4 km per hour in the same direction. A train came from behind them and crossed them in 90 and 100 seconds, respectively. The time, in seconds, taken by the train to cross an electric post is nearest to

(a) (b) (c) (d)
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Question. 12

A straight road connects points A and B. Car 1 travels from A to B and Car 2 travels from B to A, both leaving at the same time. After meeting each other, they take 45 minutes and 20 minutes, respectively, to complete their journeys. If Car 1 travels at the speed of 60 km/hr, then the speed of Car 2, in km/hr, is

(a) (b) (c) (d)
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Question. 13

A train travelled at one-thirds of its usual speed, and hence reached the destination 30 minutes after the scheduled time. On its return journey, the train initially travelled at its usual speed for 5 minutes but then stopped for 4 minutes for an emergency. The percentage by which the train must now increase its usual speed so as to reach the destination at the scheduled time, is nearest to

(a) (b) (c) (d)
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Question. 14

John gets Rs 57 per hour of regular work and Rs 114 per hour of overtime work. He works altogether 172 hours and his income from overtime hours is 15% of his income from regular hours. Then, for how many hours did he work overtime?

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Question. 15

Two ants A and B start from a point P on a circle at the same time, with A moving clock-wise and B moving anti-clockwise. They meet for the first time at 10:00 am when A has covered 60% of the track. If A returns to P at 10:12 am, then B returns to P at

(a) (b) (c) (d)
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Question. 16

Anil alone can do a job in 20 days while Sunil alone can do it in 40 days. Anil starts the job, and after 3 days, Sunil joins him. Again, after a few more days, Bimal joins them and they together finish the job. If Bimal has done 10% of the job, then in how many days was the job done?

(a) (b) (c) (d)
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Question. 17

John jogs on track A at 6 kmph and Mary jogs on track B at 7.5 kmph. The total length of tracks A and B is 325 metres. While John makes 9 rounds of track A, Mary makes 5 rounds of track B. In how many seconds will Mary make one round of track A?

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Question. 18

A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motorcycle leaves A and moves towards B. Forty-five such motorcycles reach B by 11 am. All motorcycles have the same speed. If the cyclist had doubled his speed, how many motorcycles would have reached B by the time the cyclist reached B?

(a) (b) (c) (d)
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Question. 19

The wheels of bicycles A and B have radii 30 cm and 40 cm, respectively. While traveling a certain distance, each wheel of A required 5000 more revolutions than each wheel of B. If bicycle B traveled this distance in 45 minutes, then its speed, in km per hour, was

(a) (b) (c) (d)
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Question. 20

Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If two machines can finish the job in 13 days, then how many men can finish the job in 13 days? 

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Question. 21

One can use three different transports which move at 10, 20, and 30 kmph, respectively. To reach from A to B, Amal took each mode of transport 1/3 of his total journey time, while Bimal took each mode of transport 1/3 of the total distance. The percentage by which Bimal's travel time exceeds Amal's travel time is nearest to

(a) (b) (c) (d)
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Question. 22

At their usual efficiency levels, A and B together finish a task in 12 days. If A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does, the task would have been completed in 9 days. How many days would A take to finish the task if she works alone at her usual efficiency?

(a) (b) (c) (d)
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Question. 23

Two cars travel the same distance starting at 10:00 am and 11:00 am, respectively, on the same day. They reach their common destination at the same point of time. If the first car travelled for at least 6 hours, then the highest possible value of the percentage by which the speed of the second car could exceed that of the first car is

(a) (b) (c) (d)
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Question. 24

A water tank has inlets of two types A and B. All inlets of type A when open, bring in water at the same rate. All inlets of type B, when open, bring in water at the same rate. The empty tank is completely filled in 30 minutes if 10 inlets of type A and 45 inlets of type B are open, and in 1 hour if 8 inlets of type A and 18 inlets of type B are open. In how many minutes will the empty tank get completely filled if 7 inlets of type A and 27 inlets of type B are open?

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Question. 25

Ramesh and Ganesh can together complete a work in 16 days. After seven days of working together, Ramesh got sick and his efficiency fell by 30%. As a result, they completed the work in 17 days instead of 16 days. If Ganesh had worked alone after Ramesh got sick, in how many days would he have completed the remaining work?

(a) (b) (c) (d)
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Question. 26

A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump A or pump B or both start working until the tank is full. On Monday, A alone completed filling the tank at 8 pm. On Tuesday, B alone completed filling the tank at 6 pm. On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank. At what time was the tank filled on Thursday if both pumps were used simultaneously all along?

(a) (b) (c) (d)
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Question. 27

Points A and B are 150 km apart. Cars 1 and 2 travel from A to B, but car 2 starts from A when car 1 is already 20 km away from A. Each car travels at a speed of 100 kmph for the first 50 km, at 50 kmph for the next 50 km, and at 25 kmph for the last 50 km. The distance, in km, between car 2 and B when car 1 reaches B is

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Question. 28

On a long stretch of east-west road, A and B are two points such that B is 350 km west of A. One car starts from A and another from B at the same time. If they move towards each other, then they meet after 1 hour. If they both move towards east, then they meet in 7 hrs. The difference between their speeds, in km per hour, is

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Question. 29

Let a1, a2, ... , a52 be positive integers such that a1 < a2 < ... < a52. Suppose, their arithmetic mean is one less than the arithmetic mean of a2, a3, ..., a52. If a52 = 100, then the largest possible value of a1 is

(a) (b) (c) (d)
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Question. 30

Points A, P, Q and B lie on the same line such that P, Q and B are, respectively, 100 km, 200 km and 300 km away from A. Cars 1 and 2 leave A at the same time and move towards B. Simultaneously, car 3 leaves B and moves towards A. Car 3 meets Car 1 at Q, and Car 2 at P. If each car is moving in uniform speed then the ratio of the speed of Car 2 to that of Car 1 is

(a) (b) (c) (d)
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Question. 31

A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty tank gets completely filled in 6 hours when 6 filling and 5 draining pipes are on, but this time becomes 60 hours when 5 filling and 6 draining pipes are on. In how many hours will the empty tank get completely filled when one draining and two filling pipes are on?

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Question. 32

Humans and robots can both perform a job but at different efficiencies. Fifteen humans and five robots working together take thirty days to finish the job, whereas five humans and fifteen robots working together take sixty days to finish it. How many days will fifteen humans working together (without any robot) take to finish it?

(a) (b) (c) (d)
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Question. 33

Train T leaves station X for station Y at 3 pm. Train S, traveling at three quarters of the speed of T, leaves Y for X at 4 pm. The two trains pass each other at a station Z, where the distance between X and Z is three-fifths of that between X and Y. How many hours does train T take for its journey from X to Y?

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Question. 34

Point P lies between points A and B such that the length of BP is thrice that of AP. Car 1 starts from A and moves towards B. Simultaneously, car 2 starts from B and moves towards A. Car 2 reaches P one hour after car 1 reaches P. If the speed of car 2 is half that of car 1, then the time, in minutes, taken by car 1 in reaching P from A is

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Question. 35

When they work alone, B needs 25% more time to finish a job than A does. They two finish the job in 13 days in the following manner: A works alone till half the job is done, then A and B work together for four days, and finally B works alone to complete the remaining 5% of the job. In how many days can B alone finish the entire job?

(a) (b) (c) (d)
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Question. 36

The distance from A to B is 60 km. Partha and Narayan start from A at the same time and move towards B. Partha takes four hours more than Narayan to reach B. Moreover, Partha reaches the mid-point of A and B two hours before Narayan reaches B. The speed of Partha, in km per hour, is

(a) (b) (c) (d)
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Question. 37

Amal can complete a job in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complete the job in 4 days and are paid a total amount of Rs 1000 as remuneration. If this amount is shared by them in proportion to their work, then Kamal's share, in rupees, is

(a) (b) (c) (d)
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Question. 38

A motorbike leaves point A at 1 pm and moves towards point B at a uniform speed. A car leaves point B at 2 pm and moves towards point A at a uniform speed which is double that of the motorbike. They meet at 3:40 pm at a point which is 168 km away from A. What is the distance, in km, between A and B?

(a) (b) (c) (d)
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Question. 39

A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty tank in 8 hours. If the outlet pipe is open then the inlet pipe fills the empty tank in 10 hours. If only the outlet pipe is open then in how many hours the full tank becomes half-full?

(a) (b) (c) (d)
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Question. 40

Arun drove from home to his hostel at 60 miles per hour. While returning home he drove half way along the same route at a speed of 25 miles per hour and then took a bypass road which increased his driving distance by 5 miles, but allowed him to drive at 50 miles per hour along this bypass road. If his return journey took 30 minutes more than his onward journey, then the total distance travelled by him is

(a) (b) (c) (d)
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Question. 41

A man travels by a motor boat down a river to his office and back. With the speed of the river unchanged, if he doubles the speed of his motor boat, then his total travel time gets reduced by 75%. The ratio of the original speed of the motor boat to the speed of the river is:

(a) (b) (c) (d)
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Question. 42

A man leaves his home and walks at a speed of 12 km per hour, reaching the railway station 10 minutes after the train had departed. If instead he had walked at a speed of 15 km per hour, he would have reached the station 10 minutes before the train's departure. The distance (in km) from his home to the railway station is:

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Question. 43

A person can complete a job in 120 days. He works alone on Day 1. On Day 2, he is joined by another person who also can complete the job in exactly 120 days. On Day 3, they are joined by another person of equal efficiency. Like this, everyday a new person with the same efficiency joins the work. How many days are required to complete the job? 

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Question. 44

There are three cities A, B and C, not on the same straight road. Two buses P and Q start simultaneously from A and B respectively towards C. By the time Q reaches C, P is exactly halfway to C. Immediately after Q reaches C, it starts travelling towards A and it crosses P at a point 165 km from A. The ratio of the speeds of P and Q is 3 : 5 Assume that the roads joining A to C, B to C and B to A are all straight roads. If B is twice as far from A as it is from C and P would take to cover the distance from A to B, how much time would Q take to cover the distance from C to A?

(a) (b) (c) (d)
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Question. 45

In a rowing competition, first boat rows over the course at an average speed of 4 yards/second. Second boat rows over the first half of the course at the rate of 7/2 yards / second and over the remaining half at 9/2 yards/second, thereby reaching the winning post 15 seconds after the first boat. Find the time taken (in minutes) by the second boat to cover the entire course.

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Question. 46

There is a string of length 100 m running from east to west. 1000 ants are dropped onto the string. Assume that each ant lands on the string facing either the east or the west direction. As soon as they land, each ant starts moving in the direction which is being faced by it at 50 m/ min till it falls off the string. But if an ant collides with another ant coming from the opposite direction, both of them reverse their directions and proceed to move now in the opposite directions. Ants fall only at either of the ends of the string. What is the minimum time by which the string is definitely free of ants?

(a) (b) (c) (d)
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Question. 47

P, Q and R start walking from the same point. P and Q start at 1 PM and R starts at 3 PM. R takes over P at 5 PM and then doubles his speed and takes over Q after another hour. What is the ratio of speed of A and speed of B?

(a) (b) (c) (d)
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Question. 48

Once upon a time, the king of a jungle planned a 2- kilometre race between a rabbit and a tortoise. Soon after the start of the race, the rabbit took a huge lead. On realizingthat even after taking a nap of ‘t’ min, he would beat the tortoise by 13 min, he stooped under a tree and went to sleep. Meanwhile the tortoise kept walking. When the rabbit woke up, he realized that he had slept for (14 + t) min, and immediately started running towards the target at a speed 3/2 times his original speed. The race eventually ended in a dead heat. If the ratio of the original speed of the rabbit to that of the tortoise was 6 : 1 and the rabbit overstretched his nap by [1+(1/6)] t min, then how long did the tortoise take to complete the race?

(a) (b) (c) (d)
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Question. 49

Anushka and Anirudh working together can complete a piece of work in 20 days. They started the work together, but Anushka left after x days and Anirudh finished the remaining work in the next x/2 days. Had Anushka left after 3x/4 days, Anirudh would have taken x days to finish the remaining work. Find the ratio of the efficiency of Anushka to that of Anirudh

(a) (b) (c) (d)
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Question. 50

During his trip to England, Mr. Clockilal, a horologist, decided to visit ‘The Cuckooland Museum’ dedicated to the exhibition of cuckoo clocks. He entered the museum between 12 noon and 1 p.m. The moment he entered the museum, he observed that the angle between the minute hand and the hour hand of one of the clocks was 20°. While leaving the museum, he observed that the angle between the minute hand and the hour hand of the same clock was 220°. If he spent more than 3 hours and less than 4 hours in the museum, then how much time did he exactly spend in the museum?

(a) (b) (c) (d)
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Question. 51

The radius of the cross-sections of pipes P1 and P2 are 7 m and 14 m respectively. Water flows through P1 at a constant rate of 10 m/s and it can alone fill a tank in 2 hours. If P1 is used as the inlet pipe and P2 as the outlet pipe then together they fill the tank in 4 hours. What is the rate of water flow (in m/s) through P2 ?

(a) (b) (c) (d)
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Question. 52

A train crosses a platform 100 metres long in 60 seconds at a speed of 45 km per hour. The time taken by the train (in seconds) to cross an electric pole, is

(a) (b) (c) (d)
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Question. 53

In a 400 meter race around a circular stadium having a circumference of 1000 meters, the fastest runner and the slowest runner reach the same point at the end of the 5th minute, for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken (in min.) by the fastest runner to finish the race?

(a) (b) (c) (d)
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Question. 54

A ship 55 kms. from the shore springs a leak which admits 2 tones of water in 6 min ; 80 tones would suffer to sink her, but the pumps can throw out 12 tones an hour. Find the average rate of sailing that she may just reach the shore as she begins to sink.

(a) (b) (c) (d)
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Question. 55

It takes 6 technicians a total of 10 hours to build a new server from direct computer, with each working at the same rate. If six technicians start to build the server at 11 : 00 am, and one technician per hour is added beginning at 5 :00 pm, at what time will the server be completed ?

(a) (b) (c) (d)
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Question. 56

A watch, which gains time uniformly, was 5 minutes behind the correct time when it showed 11:55 AM on Monday. It was 10 minutes ahead of the correct time when it showed 06:10 PM on the next day. When did the watch show the correct time?

(a) (b) (c) (d)
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Question. 57

A computer program was tested 300 times before its release. The testing was done in three stages of 100 tests each. The software failed 15 times in Stage I, 12 times in Stage II, 8 times in Stage III, 6 times in both Stage I and Stage II, 7 times in both Stage II and Stage III, 4 times in both Stage I and Stage III, and 4 times in all the three stages. How many times the software failed in a single stage only?

(a) (b) (c) (d)
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Question. 58

Ravi and Rahul started running from the same point in opposite directions on a circular track of length 120 m. Their speeds are 20 m/s and 40 m/s respectively. After every second, Ravi increases his speed by 2 m/s whereas Rahul decreases his speed by 2 m/s. How many times would they have met on the track by the time Rahul comes to rest?

(a) (b) (c) (d)
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Question. 59

Two friends – Tarun and Sumit – started running simultaneously from a point P in the same direction along a straight running track. The ratio of the speeds of Tarun and Sumit was 2 : 5 respectively. Two hours later, Sumit turned back and started running backwards at one-fifth of his original speed. He met Tarun at a distance of 10 km from the point P. What was Tarun’s running speed?

(a) (b) (c) (d)
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Question. 60

Ten workers started a job and worked on it for 10 days. Eleventh day onwards, a new worker joined them every day till the job was finished. It took exactly 20 days to finish the entire job. The same job has to be done starting with the minimum possible number of workers when it is known that a worker will quit the job every day after the first day. How many days will it take to finish the job in such a manner?

(a) (b) (c) (d)
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Question. 61

Rahim plans to drive from city A to station C, at the speed of 70 km per hour, to catch a train arriving there from B. He must reach C at least 15 minutes before the arrival of the train. The train leaves B, located 500 km south of A, at 8:00 am and travels at a speed of 50 km per hour. It is known that C is located between west and north-west of B, with BC at 60° to AB. Also, C is located between south and south-west of A with AC at 30° to AB. The latest time by which Rahim must leave A and still catch the train is closest to

(a) (b) (c) (d)
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Comprehension. 1

Directions for Questions: Cities A and B are in different time zones. A is located 3000 km east of B. The table below describes the schedule of an airline operating non–stop flights between A and B. All the times indicated are local and on the same day

Assume that planes cruise at the same speed in both directions. However, the effective speed is influenced by a steady wind blowing from east to west at 50 km per hour.

Question. 1

What is the plane’s cruising speed in km per hour?

(a) (b) (c) (d)
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Question. 2

What is the time difference between A and B?

(a) (b) (c) (d)
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Question. 62

Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30, 40 and 60 km per hour respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?

(a) (b) (c) (d)
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Comprehension. 2

Directions for question: Answer the questions on the basis of the information given below

Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.

Question. 1

At what time does Shyam overtake Ram?

(a) (b) (c) (d)
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Question. 2

At what time do Ram and Shyam first meet each other?

(a) (b) (c) (d)
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Question. 63

A chemical plant has four tanks (A, B, C and D) each containing 1000 litres of a chemical. The chemical is being pumped from one tank to another as follows :

From A to B @ 20 litres/minute

From C to A @ 90 litres/minute

From A to D @ 10 litres/minute

From C to D @ 50 litres/minute

From B to C @ 100 litres/minute

From D to B @ 110 litres/minute

Which tank gets emptied first, and how long does it take (in minutes) to get empty after pumping starts?

(a) (b) (c) (d)
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Question. 64

In nuts and bolts factory, one machine produces only nuts at the rate of 100 nuts per minute and needs to be cleaned for 5 minutes after production of every 1000 nuts. Another machine produces only bolts at the rate of 75 bolts per minute and needs to be cleaned for 10 minutes after production of every 1500 bolts. If both the machines start production at the same time, what is the minimum duration required for producing 9000 pairs of nuts and bolts?

(a) (b) (c) (d)
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Question. 65

Two boats, traveling at 5 and 10 kms per hour, head directly towards each other. They begin at a distance 20 kms from each other. How far apart are they (in kms) one minute before they collide?

(a) (b) (c) (d)
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Question. 66

If a man cycles at 10 km/hr, then he arrives at a certain place at 1 pm. If he cycles at 15 km/hr, he will arrive at the same place at 11 am. At what speed must he cycle to get there at noon?

(a) (b) (c) (d)
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Question. 67

Karan and Arjun run a 100-metre race, where Karan beats Arjun by 10 metres. To do a favour to Arjun, Karan starts 10 metres behind the starting line in a second 100-metre race. They both run at their earlier speeds. Which of the following is true in connection with the second race?

(a) (b) (c) (d)
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Question. 68

Two straight roads R1 and R2 diverge from a point A at an angle of 120°. Ram starts walking from point A along R1 at a uniform speed of 3 km/hr. Shyam starts walking at the same time from A along R2 at a uniform speed of 2 km/h. They continue walking for 4 hours along their respective roads and reach points B and C on R1 and R2 , respectively. There is a straight line path connecting B and C. Then Ram returns to point A after walking along the line segments BC and CA. Shyam also returns to A after walking along line segments CB and BA. Their speeds remain unchanged. The time interval (in hours) between Ram’s and shyam’s return to the point A is

(a) (b) (c) (d)
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Comprehension. 3

Directions for questions: Read the information given below and answer the questions that follow :

Consider three circular parks of equal size with centers at A1 , A2 and A3 respectively. The parks touch each other at the edge as shown in the figure (not drawn to scale). There are three paths formed by the triangles A1A2A3 , B1 B2 B3 and C1 C2 C3 as shown. Three sprinters A, B and C begin running from points A1 , B1 and C1 respectively. Each sprinter traverses her respective triangular path clockwise and returns to her starting point

Question. 1

Sprinters A, B and C traverse their respective paths at uniform speeds of u, v and w respectively. It is known that u² : v² : w² is equal to Area A : Area B : Area C, where Area A, Area B and Area C are the areas of triangles A1 A2 A3 , B1 B2 B3 and C1 C2 C3 , respectively. Where would A and C be when B reaches point B3 ?

(a) (b) (c) (d)
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Question. 2

Sprinter A traverses distances A1 A2 , A2 A3 and A3 A1 at average speeds of 20, 30 and 15, respectively. B traverses her entire path at a uniform speed of (10 3 + 20). C traverses distances C1 C2 , C2 C3 and C3 C1 at average speeds of 40/3(√3 + 1 ), 40/3(√3 + 1) and 120, respectively. All speeds are in the same unit. Where would B and C be respectively when A finishes her sprint?

(a) (b) (c) (d)
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Question. 3

Let the radius of each circular park be r, and the distances to be traversed by the sprinters A, B and C be a,b and c, respectively. Which of the following is true?

(a) (b) (c) (d)
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Question. 69

A car is being driven, in a straight line and at a uniform speed, towards the base of a vertical tower. The top of the tower is observed from the car and, in the process, it takes 10 minutes for the angle of elevation to change from 45° to 60°. After how much more time will this car reach the base of the tower?

(a) (b) (c) (d)
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Comprehension. 4

Directions for questions: Read the information given below and answer the questions that follow :

A city has two perfectly circular concentric ring roads, the outer ring road (OR) being twice as long as the inner ring road (IR) . These are also four (straight line) chord roads form E1 , the east end point of OR to N2 , the north end point of IR; from N1 , the north end point of OR to W2 , the west end point of IR, from W1, the west end point of OR, to S2 , the south end point of IR; and from S1 , the south end point of OR to E2 , the east end point of IR. Traffic moves at a constant speed of 30 km/hr on the OR road, 20 km/hr on the IR road and 15√5 km/hr on all the chord roads.

Question. 1

The ratio of the sum of the lengths of all chord roads to the length of the outer ring road is

(a) (b) (c) (d)
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Question. 2

Amit wants to reach N2 from S1. It would take him 90 minutes if he goes on minor arc S1-E1 on OR, and then on the chord road E1-N2. What is the radius of the outer ring road in kms?

(a) (b) (c) (d)
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Question. 3

Amit wants to reach E2 from N1 using first the chord N1-W2 and then the inner ring road. What will be his travel time in minutes on the basis of information given in the above question

(a) (b) (c) (d)
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Question. 70

In a 4000 metre race around a circular stadium having a circumference of 1000 metres, the fastest runner and the slowest runner reach the same point at the end of the 5th minute for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race?

(a) (b) (c) (d)
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Question. 71

A train approaches a tunnel AB. Inside the tunnel is a cat located at a point that is 3/8 of the distance AB measured from the entrance A. When the train whistles the cat runs. If the cat moves to the entrance of the tunnel, A, the train catches the cat exactly at the entrance. If the cat moves to the exit, B, the train catches the cat at exactly the exit. The speed of the train is greater than the speed of the cat by what order?

(a) (b) (c) (d)
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Question. 72

A car rental agency has following terms. If a car is rented for 5 hours or less the charge is Rs 60 per hour or Rs 12 per kilometre whichever is more. On the other hand, if the car is rented for more than 5 hours, the charge is Rs 50 per hour or Rs 7.50 per kilometre whichever is more. Akil rented a car from this agency, drove it for 30 kilometers and ended up paying Rs 300. For how many hours did he rented the Car?

(a) (b) (c) (d)
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Question. 73

On a 20 km tunnel connecting two cities A and B there are three gutters. The distance between gutter 1 and 2 is half the distance between gutter 2 and 3. The distance from City A to its nearest gutter, gutter 1 is equal to the distance of city B from gutter 3. On a particular day the hospital in city A receives information that an accident has happened at the third gutter. The victim can be saved only if an operation is started within 40 minutes. An ambulance started from city A at 30 km/hr and crossed the first gutter after 5 minutes. If the driver had doubled the speed after that, what is the maximum amount of time the doctor would get to attend the patient at the hospital? Assume 1 minute is elapsed for taking the patient into and out of the ambulance

(a) (b) (c) (d)
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Question. 74

Only a single rail track exists between station A and B on a railway line. One hour after the north bound super fast train N leaves station A for station B, a south bound passenger train S reaches station A from station B. The speed of the super fast train is twice that of a normal express train E, while the speed of a passenger train S is half that of E. On a particular day N leaves for station B from Station A, 20 minutes behind the normal schedule. In order to maintain the schedule both N and S increased their speed. If the super fast train doubles its speed, what should be the ratio (approximately) of the speed of passenger train to that of the super fast train so that passenger train S reaches exactly at the scheduled time at station A on that day

(a) (b) (c) (d)
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Question. 75

On a straight road XY, 100 metres long, five heavy stones are placed two metres apart beginning at the end X. A worker, starting at X, has to transport all the stones to Y, by carrying only one stone at a time. The minimum distance he has to travel (in metres) is

(a) (b) (c) (d)
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Question. 76

3 small pumps and a large pump are filling a tank. Each of the three small pumps works at 2/3rd the rate of the large pump. If all 4 pumps work at the same time, they should fill the tank in what fraction of the time that it would have taken the large pump alone?

(a) (b) (c) (d)
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Question. 77

6 technicians take total 10 hours to build a new server from Direct Computer, with each working at the same rate. If six technicians start to build the server at 11:00 am, and one technician per hour is added beginning at 5:00 pm, at what time will the server be complete?

(a) (b) (c) (d)
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Comprehension. 5

Directions for questions: Read the information given below and answer the questions that follow :

The petrol consumption rate of a new model car ‘Palto’ depends on its speed and may be described by the graph below.

Question. 1

Manasa would like to minimize the fuel consumption for the trip by driving at the appropriate speed. How should she change the speed?

(a) (b) (c) (d)
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Question. 2

Manasa makes the 200 km trip from Mumbai at a steady speed of 60 km per hour. What is the amount of petrol consumed for the journey?

(a) (b) (c) (d)
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Question. 78

Three runners A, B and C run a race, with runner A finishing 12 metres ahead of runner B and 18 metres ahead of runner C, while runner B finishes 8 metres ahead of C. Each runner travels the entire distance at constant speed. What was the length of the race?

(a) (b) (c) (d)
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Question. 79

A train X departs from station A at 11.00 am for station B, which is 180 km away. Another train Y departs from station B at 11.00 am for station A. Train X travels at an average speed of 70 kms/hr and does not stop any where until it arrives at station B. Train Y travels at an average speed of 50 kms/hr, but has to stop for 15 minutes at station C, which is 60 kms away from station B enroute to station A. Ignoring the lengths the train , what is the distance , to the nearest km, from station A to the point where the trains cross each other?

(a) (b) (c) (d)
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Question. 80

There’s a lot of work in preparing a birthday dinner. Even after the turkey is in the oven, there’s still the potatoes and gravy, yams, salad, and cranberries, not to mention setting the table. Three friends, Asit, Arnold, and Afzal, work together to get all of these chores done. The time it takes them to do the work together is six hours less than Asit would have taken working alone, one hour less than Arnold would have taken alone, and half the time Afzal would have taken working alone. How long did it take them to do these chores working together?

(a) (b) (c) (d)
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Question. 81

Shyama and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps for every two of Vyom’s steps. Shyama gets to the top of the escalator after having taken 25 steps, while Vyom (because his slower pace lets the escalator do a little more of the work) takes only 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up?

(a) (b) (c) (d)
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Question. 82

At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in six hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for this 24 mile round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles. What is the speed of the current in miles per hour?

(a) (b) (c) (d)
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Question. 83

If 09/12/2001 happens to be Sunday, then 09/12/1971 would have been

(a) (b) (c) (d)
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Question. 84

A can complete a piece of work in 4 days. B takes double the times taken by A, C takes double that of B, and D takes double that of C to complete the same task. They are paired in groups of two each. One pair takes two- third the time needed by the second pair to complete the work. Which is the first pair?

(a) (b) (c) (d)
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Question. 85

The vehicle of Mr. Ghosh needs 30% more fuel at the speed of 75 kmph than it needs at the speed of 50 kmph. At a speed of 50 kmph, Mr. Ghosh can go to a distance of 195 kms. At the speed of 75 kmph, he will able to travel a distance of

(a) (b) (c) (d)
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Comprehension. 6

Directions for questions: Read the information given below and answer the questions that follow :

There are five machines A, B, C, D and E – situated on a straight line at distances of 10 m, 20 m, 30 m, 40 m and 50 m respectively from the origin of the line. A robot is stationed at the origin of the line. The robot serves the machines with raw material whenever a machine becomes idle. All the raw materials are located at the origin. The robot is in an idle state at the origin at the beginning of a day. As soon as one or more machines become idle, they send messages to the robot-station and the robot starts and serves all the machines from which it received messages. If a message is received at the station while the robot is away from it, the robot takes notice of the message only when it returns to the station. While moving, it serves the machines in the sequence in which they are encountered, and then returns to the origin. If any messages are pending at the station when it returns, it repeats the process again. Otherwise, it remains idle at the origin till the next message(s) is/are received.

Question. 1

Suppose there is a second station with raw material for the robot at the other extreme of the line which is 60 m from the origin, i.e., 10 m from E. After finishing the services in a trip, the robot returns to the nearest station. If both stations are equidistant, it chooses the origin as the station to return to. Assuming that both stations receive the message sent by the machines and that all the other data remains the same, what would be the answer to the above question?

(a) (b) (c) (d)
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Question. 2

Suppose on a certain day, machines A and D have sent the first two messages to the origin at the beginning of the 1st second, C has sent a message at the beginning of the 5th second, B at the beginning of the 6th second and E at the beginning of the 10th second. How much distance has the robot travelled since the beginning of the day, when it notices the message of E? Assume that the speed of movement of the robot is 10 m/s.

(a) (b) (c) (d)
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Question. 86

A and B are two cities 10 km apart. A load of 80 kg has to be transported form A to B. The courier service charges @ 10Rs per hour. The optimal speed that one can go without load is 10 km/hr, the speed reduces to 5 km/hr with a weight of 10 Kg. Further with 20 kg (which is the maximum weight that can be carried), the speed is 2 km/hr. what is the minimum cost?

(a) (b) (c) (d)
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Comprehension. 7

Directions for questions: Read the information given below and answer the questions that follow :

There is a network of routes as shown in the figure given below. D is the mid point of AC, AB is perpendicular to BC and AB = 100km. The persons, X & Y, go from A to C, starting at the same time and reaching at the same time. X follows the path A-B-C with an average speed of 61.875 kmph, and Y follows the straight path A-C, covering part AD at 45 kmph and part DC at 55 Kmph.

Question. 1

What is the distance A-C

(a) (b) (c) (d)
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Question. 2

What is the distance B-C?

(a) (b) (c) (d)
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Question. 3

What is the average speed of Y between A-C

(a) (b) (c) (d)
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Question. 87

A railway engine moves with the speed of 42 kmph. The reduction in speed varies as the square root of the number of compartments attached to it. The speed is 24 kmph when 9 compartments are attached. What is the maximum number of compartments that the engine can pull?

(a) (b) (c) (d)
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Question. 88

Navjeeven exp., which goes form Ahmedabad to Chennai leaves Ahmedabad at 6:30 am and travels at a constant speed of 50 kmph towards Baroda, which is 100 kms away. At 7:00, the How -Ambd exp. leaves for Ahmedabad from Baroda at a constant speed of 40 kmph. At 7:30 Mr. Shah, the control officer, realises that both the trains are on the same track. How much time does Mr. Shah have to avert the accident?

(a) (b) (c) (d)
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Comprehension. 8

Directions for questions: Read the information given below and answer the questions that follow :

Rajiv travels to B from A in 4 hrs. travelling at 35 kmph for two hrs and at 45 kmph for the next two hrs. Aditi travels on the same route at speeds of 30, 40 and 50 kmph, covering equal distances at each of these speeds. The relation between fuel consuption and speed is given in the following graph.

Question. 1

Zorin would like to drive Aditi’s car over the same route form A to B. minimize the petrol consumption for the trip. The amount of petrol required by him is

(a) (b) (c) (d)
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Question. 2

How many litres of fuel is consumed by Aditi

(a) (b) (c) (d)
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Question. 89

I started climbing up the hill at 6 am and reached the temple at the top at 6 pm Next day I started coming down at 6 am and reached the foothill at 6 pm. I walked on the same road. The road is so short that only one person can walk on it. Although I varied my pace on my way, I never stopped on my way. Then which of the following must be true

(a) (b) (c) (d)
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Question. 90

Distance between A and B is 72 km. Two men started walking from A and B at the same time towards each other. The person who started from A travelled uniformly with average speed 4 kmph. While the other man travelled with varying speeds as follows : In first hour his speed was 2 kmph, in the second hour it was 2.5 kmph, in the third hour it was 3 kmph, and so on. When will they meet each other?

(a) (b) (c) (d)
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Question. 91

A company has a job to prepare certain no. of cans and there are three machines A, B & C for this job. A can complete the job in 3 days, B can complete the job in 4 days and C can complete the job in 6 days. How many days the company will take to complete job if all the machines are used simultaneously?

(a) (b) (c) (d)
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Comprehension. 9

Directions for questions: Read the information given below and answer the questions that follow :

A thief, after committing the burglary, started fleeing at 12:00 noon, at the speed of 60 kmph. He was then chased by a policeman X. X started the chase 15 minutes after the thief had started, at a speed of 65 kmph.

Question. 1

If another policeman had started the same chase along with X, but at a speed of 60 kmph, then how far behind was he when X caught the thief?

(a) (b) (c) (d)
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Question. 2

At what time did X catch the thief?

(a) (b) (c) (d)
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Question. 92

Boston is 4 hours ahead of Frankfurt and two hours behind India. X leaves Frankfurt at 06:00 pm on Friday and reaches Boston the next day. After waiting there for two hours, he leaves exactly at noon and reaches India at 01:00 am. On his return journey, he takes the same route as before, but halts at Boston for one hour less than his previous halt there. He then proceeds to Frankfurt.

What was X’s average speed for the entire journey?

(a) (b) (c) (d)
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Question. 93

Boston is 4 hours ahead of Frankfurt and two hours behind India. X leaves Frankfurt at 06:00 pm on Friday and reaches Boston the next day. After waiting there for two hours, he leaves exactly at noon and reaches India at 01:00 am. On his return journey, he takes the same route as before, but halts at Boston for one hour less than his previous halt there. He then proceeds to Frankfurt.

If his journey, including stoppages, was covered at an average speed of 180 miles per hour, what was the distance between Frankfurt and India?

(a) (b) (c) (d)
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Question. 94

Boston is 4 hours ahead of Frankfurt and two hours behind India. X leaves Frankfurt at 06:00 pm on Friday and reaches Boston the next day. After waiting there for two hours, he leaves exactly at noon and reaches India at 01:00 am. On his return journey, he takes the same route as before, but halts at Boston for one hour less than his previous halt there. He then proceeds to Frankfurt.

 If X had started his return journey from India at 02:55 am on the same day that he reached there, after how much time would he reach Frankfurt?

(a) (b) (c) (d)
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Question. 95

An express train travelling at 80 kmph overtakes a goods train, twice as long and going at 40 kmph on a parallel track, in 54 seconds. How long will the express train take to cross a station 400 m long?

(a) (b) (c) (d)
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Question. 96

In a mile race, Akshay can be given a start of 128 metres by Bhairav. If Bhairav can give Chinmay a start of 4 metres in a 100 metres dash, then who out of Akshay and Chinmay will win a race of one and a half mile, and what will be the final lead given by the winner to the loser? (one mile is 1600 metres)

(a) (b) (c) (d)
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Question. 97

In a watch, the minute hand crosses the hour hand for the third time exactly after every 3 hrs., 18 min., 15 seconds of watch time. What is the time gained or lost by this watch in one day?

(a) (b) (c) (d)
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Question. 98

A man travels from A to B at a speed of x kmph. He then rests at B for x hours. He then travels from B to C at a speed of 2x kmph and rests at C for 2x hours. He moves further to D at a speed twice as that between B and C. He thus reaches D in 16 hours. If distances A-B, B-C, C-D are all equal to 12 km, the time for which he rested at B could be

(a) (b) (c) (d)
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Question. 99

A man travels three-fifths of a distance AB at a speed of 3a, and the remaining at a speed of 2b. If he goes from B to A and back at a speed of 5c in the same time, then

(a) (b) (c) (d)
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Question. 100

Persons X, Y and Z wish to go from place A to place B, which are separated by a distance of 70 km. All the three persons start off together from A, with X and Y going by Luna at a speed of 20 kmph. X drops Y somewhere along the way and returns to pick up Z, who has already started walking towards B at a speed of 5 kmph. Y, after being dropped by X, starts walking towards B at a speed of 5 kmph. In this manner, all three of them reach B at the same time.

How long does it take them to go from A to B?

(a) (b) (c) (d)
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Question. 101

Persons X, Y and Z wish to go from place A to place B, which are separated by a distance of 70 km. All the three persons start off together from A, with X and Y going by Luna at a speed of 20 kmph. X drops Y somewhere along the way and returns to pick up Z, who has already started walking towards B at a speed of 5 kmph. Y, after being dropped by X, starts walking towards B at a speed of 5 kmph. In this manner, all three of them reach B at the same time.

What is the total distance travelled by x?

(a) (b) (c) (d)
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Question. 102

Persons X, Y and Z wish to go from place A to place B, which are separated by a distance of 70 km. All the three persons start off together from A, with X and Y going by Luna at a speed of 20 kmph. X drops Y somewhere along the way and returns to pick up Z, who has already started walking towards B at a speed of 5 kmph. Y, after being dropped by X, starts walking towards B at a speed of 5 kmph. In this manner, all three of them reach B at the same time.

How much distance is covered by Z on foot?

(a) (b) (c) (d)
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Question. 103

A and B are running along a circular course of radius 7 km in opposite directions such that when they meet they reverse their directions and when they meet A will run at the speed of B and vice-versa. Initially, the speed of A is thrice the speed of B. Assume that they start from M0 and they first meet at M1 , then at M2 , next at M3 , and finally at M4

What is the shortest distance between M1 and M2 ?

(a) (b) (c) (d)
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Question. 104

A and B are running along a circular course of radius 7 km in opposite directions such that when they meet they reverse their directions and when they meet A will run at the speed of B and vice-versa. Initially, the speed of A is thrice the speed of B. Assume that they start from M0 and they first meet at M1 , then at M2 , next at M3 , and finally at M4

What is the shortest distance between M1 and M3 along the course?

(a) (b) (c) (d)
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Question. 105

In a race of 200 metres run, A beats S by 20 metres and N by 40 metres. If S and N are running a race of 100 metres with exactly same speed as before then, by how many metres will S beat N ?

(a) (b) (c) (d)
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Question. 106

The winning relay team in a high school sports competition clocked 48 minutes for a distance of 13.2 km. Its runners A, B, C and D maintained speeds of 15 kmph, 16 kmph, 17 kmph, and 18 kmph respectively. What is the ratio of the time taken by B to time taken by D?

(a) (b) (c) (d)
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Question. 107

There is leak in the bottom of a tank. This leak can empty a full tank in 8 hours. When the tank is full, a tap is opened into the tank which admits 6 litres per hour and the tank is now emptied in 12 hours. What is the capacity of the tank?

(a) (b) (c) (d)
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Question. 108

A and B walk from X to Y, a distance of 27 km at 5 kmph and 7 kmph respectively. B reaches Y and immediately turns back meeting A at Z. What is the distance from X to Z?

(a) (b) (c) (d)
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Question. 109

A water tank has three taps A, B and C. A fills four buckets in 24 minutes, B fills 8 buckets in 1 hour and C fills 2 buckets in 20 minutes. If all the taps are opened together a full tank is emptied in 2 hours. If a bucket can hold 5 litres of water, what is the capacity of the tank?

(a) (b) (c) (d)
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Question. 110

Four friends start from four towns, which are at the four corners of an imaginary rectangle. They meet at a point which falls inside the rectangle, after travelling distances of 40, 50, and 60 metres. The maximum distance that the fourth could have travelled is (approximately)

(a) (b) (c) (d)
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Question. 111

One man can do as much work in one day as a woman can do in 2 days. A child does one third the work in a day as a woman. If an estate-owner hires 39 pairs of hands, men, women and children in the ratio 6 : 5 : 2 and pays them in all Rs 1113 at the end of the days work. What must be the daily wage of a child, if the wages are proportional to the amount of work done?

(a) (b) (c) (d)
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Question. 112

It takes the pendulum of a clock 7 seconds to strike 4 o’clock. How much time will it take to strike 11 o’clock?

(a) (b) (c) (d)
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Question. 113

Two towns A and B are 100 km apart. A school is to be built for 100 students of town B and 30 students of town A. Expenditure on transport is Rs 1.20 per km per student. If the total expenditure on transport by all 130 students is to be as small as possible, then the school should be built at 

(a) (b) (c) (d)
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Question. 114

Shyam went from Delhi to Simla via Chandigarh by car. The distance from Delhi to Chandigarh is 3/4 times the distance from Chandigarh to Simla. The average speed from Delhi to Chandigarh was half as much again as that from Chandigarh to Simla. If the average speed for the entire journey was 49 kmph. What was the average speed from Chandigarh to Simla?

(a) (b) (c) (d)
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