### Question. 1

A person invested a certain amount of money at 10% annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs 18522. The amount, in rupees, that the person had invested is

A person invested a certain amount of money at 10% annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs 18522. The amount, in rupees, that the person had invested is

Two alcohol solutions, A and B, are mixed in the proportion 1:3 by volume. The volume of the mixture is then doubled by adding solution A such that the resulting mixture has 72% alcohol. If solution A has 60% alcohol, then the percentage of alcohol in solution B is

A man buys 35 kg of sugar and sets a marked price in order to make a 20% profit. He sells 5 kg at this price, and 15 kg at a 10% discount. Accidentally, 3 kg of sugar is wasted. He sells the remaining sugar by raising the marked price by p percent so as to make an overall profit of 15%. Then p is nearest to

In the final examination, Bishnu scored 52% and Asha scored 64%. The marks obtained by Bishnu is 23 less, and that by Asha is 34 more than the marks obtained by Ramesh. The marks obtained by Geeta, who scored 84%, i

In May, John bought the same amount of rice and the same amount of wheat as he had bought in April, but spent 150 more due to price increase of rice and wheat by 20% and 12%, respectively. If John had spent 450 on rice in April, then how much did he spend on wheat in May?

Anil buys 12 toys and labels each with the same selling price. He sells 8 toys initially at 20% discount on the labeled price. Then he sells the remaining 4 toys at an additional 25% discount on the discounted price. Thus, he gets a total of Rs 2112, and makes a 10% profit. With no discounts, his percentage of profit would have been

For the same principal amount, the compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by Rs 1125. Then the principal amount in rupees is

In a group of people, 28% of the members are young while the rest are old. If 65% of the members are literates, and 25% of the literates are young, then the percentage of old people among the illiterates is nearest to

A person spent Rs 50000 to purchase a desktop computer and a laptop computer. He sold the desktop at 20% profit and the laptop at 10% loss. If overall he made a 2% profit then the purchase price, in rupees, of the desktop is

Veeru invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal?

A shopkeeper sells two tables, each procured at cost price p, to Amal and Asim at a profit of 20% and at a loss of 20%, respectively. Amal sells his table to Bimal at a profit of 30%, while Asim sells his table to Barun at a loss of 30%. If the amounts paid by Bimal and Barun are x and y, respectively, then (x - y) / p equals

Amal invests Rs 12000 at 8% interest, compounded annually, and Rs 10000 at 6% interest, compounded semi-annually, both investments being for one year. Bimal invests his money at 7.5% simple interest for one year. If Amal and Bimal get the same amount of interest, then the amount, in Rupees, invested by Bimal is

The strength of a salt solution is p% if 100 ml of the solution contains p grams of salt. Each of three vessels A, B, C contains 500 ml of salt solution of strengths 10%, 22%, and 32%, respectively. Now, 100 ml of the solution in vessel A is transferred to vessel B. Then, 100 ml of the solution in vessel B is transferred to vessel C. Finally, 100 ml of the solution in vessel C is transferred to vessel A. The strength, in percentage, of the resulting solution in vessel A is

Mukesh purchased 10 bicycles in 2017, all at the same price. He sold six of these at a profit of 25% and the remaining four at a loss of 25%. If he made a total profit of Rs. 2000, then his purchase price of a bicycle, in Rupees, was

In an examination, the score of A was 10% less than that of B, the score of B was 25% more than that of C, and the score of C was 20% less than that of D. If A scored 72, then the score of D was

In 2010, a library contained a total of 11500 books in two categories - fiction and non-fiction. In 2015, the library contained a total of 12760 books in these two categories. During this period, there was 10% increase in the fiction category while there was 12% increase in the non-fiction category. How many fiction books were in the library in 2015?

The income of Amala is 20% more than that of Bimala and 20% less than that of Kamala. If Kamala's income goes down by 4% and Bimala's goes up by 10%, then the percentage by which Kamala's income would exceed Bimala's is nearest to

On selling a pen at 5% loss and a book at 15% gain, Karim gains Rs. 7. If he sells the pen at 5% gain and the book at 10% gain, he gains Rs. 13. What is the cost price of the book in Rupees?

A person invested a total amount of Rs 15 lakh. A part of it was invested in a fixed deposit earning 6% annual interest, and the remaining amount was invested in two other deposits in the ratio 2 : 1, earning annual interest at the rates of 4% and 3%, respectively. If the total annual interest income is Rs 76000 then the amount (in Rs lakh) invested in the fixed deposit was

Meena scores 40% in an examination and after review, even though her score is increased by 50%, she fails by 35 marks. If her post-review score is increased by 20%, she will have 7 marks more than the passing score. The percentage score needed for passing the examination is

In a class, 60% of the students are girls and the rest are boys. There are 30 more girls than boys. If 68% of the students, including 30 boys,pass an examination, the percentage of the girls who do not pass is

Gopal borrows Rs. X from Ankit at 8% annual interest. He then adds Rs. Y of his own money and lends Rs. X+Y to Ishan at 10% annual interest. At the end of the year, after returning Ankit’s dues, the net interest retained by Gopal is the same as that accrued to Ankit. On the other hand, had Gopal lent Rs. X+2Y to Ishan at 10%, then the net interest retained by him would have increased by Rs. 150. If all interests are compounded annually, then find the value of X + Y.

Gopal borrows Rs. X from Ankit at 8% annual interest. He then adds Rs. Y of his own money and lends Rs. X+Y to Ishan at 10% annual interest. At the end of the year, after returning Ankit’s dues, the net interest retained by Gopal is the same as that accrued to Ankit. On the other hand, had Gopal lent Rs. X+2Y to Ishan at 10%, then the net interest retained by him would have increased by Rs. 150. If all interests are compounded annually, then find the value of X + Y.

A jar contains a mixture of 175 ml water and 700 ml alcohol. Gopal takes out 10% of the mixture and substitutes it by water of the same amount. The process is repeated once again. The percentage of water in the mixture is now

In an examination, the maximum possible score is N while the pass mark is 45% of N. A candidate obtains 36 marks, but falls short of the pass mark by 68%. Which one of the following is then correct?

John borrowed Rs. 2,10,000 from a bank at an interest rate of 10% per annum, compounded annually. The loan was repaid in two equal instalments, the first after one year and the second after another year. The ﬁrst instalment was interest of one year plus part of the principal amount, while the second was the rest of the principal amount plus due interest thereon. Then each instalment, in Rs., is

In a village, the production of food grains increased by 40% and the per capita production of food grains increased by 27% during a certain period. The percentage by which the population of the village increased during the same period is nearest to

Mayank buys some candies for Rs 15 a dozen and an equal number of different candies for Rs 12 a dozen. He sells all for Rs 16.50 a dozen and makes a profit of Rs 150. How many dozens of candies did he buy altogether?

The manufacturer of a table sells it to a wholesale dealer at a profit of 10%. The wholesale dealer sells the table to a retailer at a profit of 30%. Finally, the retailer sells it to a customer at a profit of 50%. If the customer pays Rs 4290 for the table, then its manufacturing cost (in Rs) is

Out of the shirts produced in a factory, 15% are defective, while 20% of the rest are sold in the domestic market. If the remaining 8840 shirts are left for export, then the number of shirts produced in the factory is

If Fatima sells 60 identical toys at a 40% discount on the printed price, then she makes 20% profit. Ten of these toys are destroyed in fire. While selling the rest, how much discount should be given on the printed price so that she can make the same amount of profit?

In a market, the price of medium quality mangoes is half that of good mangoes. A shopkeeper buys 80 kg good mangoes and 40 kg medium quality mangoes from the market and then sells all these at a common price which is 10% less than the price at which he bought the good ones. His overall profit is:

The number of girls appearing for an admission test is twice the number of boys. If 30% of the girls and 45% of the boys get admission, the percentage of candidates who do not get admission is:

If a seller gives a discount of 15% on retail price, she still makes a profit of 2%. Which of the following ensures that she makes a profit of 20%?

Ravi invests 50% of his monthly savings in fixed deposits. Thirty percent of the rest of his savings is invested in stocks and the rest goes into Ravi's savings bank account. If the total amount deposited by him in the bank (for savings account and fixed deposits) is Rs 59500, then Ravi's total monthly savings (in Rs) is:

Some friends planned to contribute equally to jointly buy a CD player. However, two of them decided to withdraw at the last minute. As a result, each of the others had to shell out one rupee more than what they had planned for. If the price (in Rs.) of the CD player is an integer between 1000 and 1100, find the number of friends who actually contributed?

Balram, the local shoe shop owner, sells four types of footwear – Slippers (S), Canvas Shoes (C), Leather Shoes (L) and Joggers (J). The following information is known regarding the cost prices and selling prices of these four types of footwear:

(i) L sells for Rs. 500 less than J, which costs Rs. 300 more than S, Which, in turn, sells for Rs.200 more than L.

(ii) L costs Rs. 300 less than C, which sells for Rs. 100 more than S, which, in turn, costs Rs. less than C.

If it is known that Balram never sells any item at a loss, then which of the following is true regarding the profit percentages earned by Balram on the items L, S, C and J represented by l, s, c and j

The total cost of 2 pencils, 5 erasers, and 7 sharpeners is Rs. 30, while 3 pencils and 5 sharpeners cost Rs. 15 more than 6 erasers. By what amount (in Rs.) does the cost of 39 erasers and 1 sharpener exceed the cost of 6 pencils?

A shopkeeper sold 10 items, all of which are of the same cost price, such that profit percentage on no two item is the same. The profits made on the given items were in an arithmetic progression. If the profit percentage of the item the selling price of which is 4th highest and the item the selling price of which is 7th highest were 13 % and 10 % respectively, find the profit percentage on the whole.

There are two factories – A and B – in Kaarobaarnagar. In factory A, the number of male employees is 50% more than that of female employees. In factory B, the number of female employees is 40% less than that of male employees. The number of female employees in factory B is 60 more than that of male employees in factory A. Which of the following cannot be the total number of male employees in the two factories put together?

The percentage volumes of milk in three solutions A, B and C from a geometric progression in the order. If we mix the first, second and third solutions in the ratio 2 : 3 : 4 by volume, we obtain a solution containing 32% milk. If we mix them in the ratio 3 : 2 : 1, by volume, we obtain a solution containing 22% milk, What is the percentage of milk in A ?

An empty metal container (without its handle) weighs 15% of what it weighs when completely filled with a particular liquid. After adding the handle, the weight of the fully filled container increases by 5%. If the weight of a partly filled container is 1/3 of the completely filled container with the handle attached, then what fraction of container is utilized

A trader used to make 5% profit on an item by selling it at the usual marked price. One day, he tripled the marked price of the item and finally offered a discount of 30%. Find the percentage profit he made on the item that day.

A shopkeeper sells four qualities of rice A, B, C and D having cost price Rs.40/kg,Rs. 55/kg, Rs.50/kg and R.s65/kg respectively. Ankit purchased ‘a’ kg of A and ‘b’ kg of B to make ‘a + b’ kg of a new quality ‘E’ of rice worth ` 50/kg. Then he purchased ‘c’ kg of C and ‘d’ kg of D to make ‘c + d’ kg of a new quality ‘F’ of rice worth Rs.60/kg. Finally he took ‘x’ kg of rice and ‘y’ kg of rice from ‘E’ quality of rice and ‘F’ quality of rice respectively to make ‘x + y’ kg of rice worth Rs. 53/kg. Ensuring that a, b, c, d, x and y are all integers then what is the minimum value of a + b + c + d + x + y in kg?

A contractor did not have space in his garage for 8 of his trucks. He, therefore, increased the size of his garage by 50% which gave him space for 8 more trucks than he owned altogether. How many trucks did he own?

The list price of an article was increased by 10%. It was then decreased by 10%. If the final price became Rs. 20, then find the initial list price (in Rs.)

10% of the voters did not cast their vote in an election between two candidates. 10% of the votes polled were found invalid. The successful candidate got 54% of the valid votes and won by a majority of 1620 votes. The number of voters enrolled on the voters list was :

Ramit sold a table at a profit of 15%. Had he bought it at 10% less and sold it for Rs.21 less, he would have gained 25%. At what price (in Rs.) had he bought the table?

Mr. Mehra is planning for higher education expenses of his two sons aged 15 and 12. He plans to divide ` 15 lakhs in two equal parts and invest in two different plans such that his sons may have access to ` 21 lakhs each when they reach the age of 21. He is looking for plan that will give him a simple interest per annum. The rates of interest of the plans for his younger son and elder son should be

In an examination, the average marks obtained by students who passed was x %, while the average of those who failed was y %. The average marks of all students taking the exam was z %. Find in terms of x, y and z, the percentage of students taking the exam who failed.

There are three water-alcohol solutions A, B and C whose alcohol concentrations are 50%, 60% and 70% respectively. x ml of A, (x + 2) ml of B and (x + 3) ml of C are mixed. If the alcohol concentration of the resultant mixture is 65%, then x lies in the range

A person closes his account in an investment scheme by withdrawing Rs. 10,000. One year ago he had withdrawn Rs. 6000. Two years ago he had withdrawn Rs. 5000. Three years ago he had not withdrawn any money. How much money had he deposited approximately at the time of opening the account 4 years ago, if the annual simple interest is 10% ?

**Directions for Questions:** Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, each of which can be utilized fully or partially in conjunction with others.

**Option A:** Invest in a public sector bank. It promises a return of +0.10%.

**Option B:** Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5%, while a fall will entail a return of –3%.

**Option C:** Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of –2.5%, while a fall will entail a return of +2%.

What strategy will maximize the guaranteed return to Shabnam?

The maximum guaranteed return to Shabnam is

A leather factory produces two kinds of bags, standard and deluxe bag. The profit margin is Rs 20 on a standard bag and Rs 30 on a deluxe bag. Every bag must be processed on machine A and on machine B. The processing times per bag on the two machines are as follows:

The total time available on machine A is 700 hours and on machine B is 1250 hours. Among the following production plans, which one meets the machine availability constraints and maximizes the profit?

At the end of year 1998, Shepard bought nine dozen goats. Henceforth, every year he added p% of the goats at the beginning of the year and sold q % of the goats at the end of the year where p > 0 and q > 0. If Shepard had nine dozen goats at the end of year 2002, after making the sales for that year, which of the following is true?

Davji Shop sells Samosas in boxes of different sizes. The Samosas are priced at Rs 2 per Samosa up to 200 Samosas. For every additional 20 Samosas, the price of the whole lot goes down by 10 paise per Samosa. What should be the maximum size of the box that would maximise the revenue?

The owner of an art shop conducts his business in the following manner. Every once in a while he raises his prices by X %, then a while later he reduces all the new prices by X %. After one such up-down cycle, the price of a painting decreased by Rs 441. After a second up-down cycle the painting was sold for Rs 1944.81. What was the original price of the painting?

A college has raised 75% of the amount it needs for a new building by receiving an average donation of Rs 600 from the people already solicited. The people already solicited represent 60% of the people, the college will ask for donations. If the college is to raise exactly the amount needed for the new building, what should be the average donation from the remaining people to be solicited?

A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is

What number of widgets being 0-60 which of the following is true?

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

The following graph represents the variable cost of widgets as a function of quantity produced. The cost of production has two components, variable cost — which is given in the graph, and fixed cost — which is Rs 800 for the first shift in which 30 widgets can be produced and if more production is desired then a second shift is started which can produce an additional 30 widgets.

The fixed cost of the second shift is Rs 1200.

Average cost is defined as the total cost total number of the widgets

Marginal cost is defined as change in total cost change in number of widgets produced.

What number of widgets give the maximum profit?

What is the total cost of production in July?

If the number of widgets increase form 40 in July to 41 in September what is the marginal cost ?

What is the average cost if number of widgets in July is 40?

In a company 40% are male, out of which 75% earn a salary of 25,000 plus. If 45% of the employees 25,000 plus salaries, what is the fraction of female employees earning less than or equal to 25,000?

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

A company purchases components A and B from Germany and USA respectively. A and B form 30% and 50% of the total production cost. Current gain is 20%. Due to change in the international scenario, cost of the German Mark increased by 30% and that of USA Dollar increased by 22%. Due to market conditions the selling price cannot be increased beyond 10%. Then

If the USA Dollar becomes cheap by 12% over its original cost and the cost of German Mark increased by 20%. The selling price is not altered. What will be the gain?

What is the maximum current gain possible?

One bacterium splits into eight bacteria of the next generation. But due to environment only 50% of one generation can produce the next generation. If the seventh generation number is 4096 million, then what is the number in first generation?

A company purchases components A and B from Germany and USA respectively. A and B form 30% and 50% of the total production cost. Current gain is 20%. Due to change in the international scenario, cost of the German Mark increased by 30% and that of USA Dollar increased by 22%. Due to market conditions the selling price cannot be increased beyond 10%. Then

If the USA Dollar becomes cheap by 12% over its original cost and the cost of German Mark increased by 20%. The selling price is not altered. What will be the gain?

A company purchases components A and B from Germany and USA respectively. A and B form 30% and 50% of the total production cost. Current gain is 20%. Due to change in the international scenario, cost of the German Mark increased by 30% and that of USA Dollar increased by 22%. Due to market conditions the selling price cannot be increased beyond 10%. Then

What is the maximum current gain possible?

One bacterium splits into eight bacteria of the next generation. But due to environment only 50% of one generation can produce the next generation. If the seventh generation number is 4096 million, then what is the number in first generation?

A man earns x % on the first 2000 rupees and y % on the rest of his income. If he earns Rs 700 from Rs 4000 and Rs 900 from Rs 5000 of income, find x

Fresh grapes contain 90% water while dry grapes contain 20% water. What is the weight of dry grapes obtained from 20 kg of fresh grapes?

After allowing a discount of 11.11%, a trader still makes a gain of 14.28%. At how many per cent above the cost price does he mark his goods?

A student gets an aggregate of 60% marks in five subjects in the ratio 10:9:8:7:6. If the passing marks are 50% of the maximum marks and each subject has the same maximum marks, in how many subjects did he pass the exam?

Instead of a metre scale cloth merchant uses a 120 cm scale while buying but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20 per cent of cash payment, what is his overall per cent profit?

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

A watch dealer incurs an expense of Rs 150 for producing every watch. He also incurs an additional expenditure of Rs30, 000, which is independent of the number of watches produced. If he is able to sell a watch during the season, he sells it for Rs 250. If he fails to do so, he has to sell each watch for Rs 100.

If he produces 1500 watches, what is the number of watches that he must sell during the season in order to break even, given that he is able to sell all the watches produced?

If he is able to sell only 1200 out of the 1500 watches he has made in the season, then in the season he has made a profit of

The cost of a diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1:2:3:4. When the pieces were sold, the merchant got Rs 70,000 less. Find the original price of the diamond.

The price of a Maruti Car rises by 30% while the sales of the car come down by 20%. What is the per cent change in the total revenue?

I sold two watches for Rs 300 each, one at a loss of 10% and the other at a profit of 10%. What is the per cent loss (–) or the per cent profit (+) that resulted from the transaction ?

2/5 of the voters promise to vote for P and the rest promised to vote for Q. Of these, on the last day 15% of the voters went back of their promise to vote for P and 25% of voters went back of their promise to vote for Q and P lost by 2 votes. Then the total number of voters is

A man invests Rs 3000 at a rate of 5% per annum. How much more should he invest at a rate of 8%, so that he can earn a total of 6% per annum ?

The rate of inflation was 1000%. Then, what will be cost of an article, which costs 6 units of currency now, two years from now?

Ram purchased a flat at Rs 1 lakh and Prem purchase a plot of land worth Rs 1.1 lakh. The respective annual rates at which the prices of the falt and the plot increased were 10 % and 5%. After two years they exchanged their belongings and one paid the other the difference. Then...

A person who has a certain amount with him goes to the market. He can buy 50 oranges or 40 mangoes. He retains 10% of the amount as taxi fare and buys 20 mangoes and of the balance he purchases oranges. Number of oranges he can purchase is

Last week Martin received $ 10 in commission for selling 100 copies of a magazine. Last week Miguiel sold 100 copies of this magazine. He received his salary of $ 5 per week plus a commission of 2 cents for each of the first 25 copies sold, 3 cents for each of next 25 copies sold and 4 cents for each copy thereafter. ($1 = 100 cents) (1994)

I. Martin’s commission in the last week

II. Miguiel’s total income for last week

A dealer offers a cash discount of 20% and still makes a profit of 20%, when he further allows 16 articles to a dozen to a particularly sticky bargainer. How much per cent above the cost price were his wares listed?

The number of votes not cast for the Praja Party increased by 25% in the National General Elections over those not cast for it in the previous Assembly Polls, and the Praja Party lost by a majority twice as large as that by which it had won the Assembly Polls. If a total of 2,60,000 people voted each time, how many voted for the Praja Party in the Assembly Elections?