CAT Quantitative Ability Questions | CAT TIme, Speed, Distance and Work questions

Comprehension

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.

CAT/2000

Question . 108

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.

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Explanatory Answer

Method of solving this CAT Quantitative Ability Question from TIme, Speed, Distance and Work question

(a) The installation and functioning of all the five machines will be as per the following figure.

The robot begins to give material to machine A and then to D, thus it covers 40 m in that time span and takes 4 seconds.

Also it returns to the origin at the same time and takes 4 seconds covering 40 metres again.

When it arrives at the origin the messages of B and C are already present there.

Hence it starts to deliver the material to them taking in all 6 seconds in doing so and covers 30 + 30 = 60 metres. Hence the distance travelled by the robot will be 40m + 40m + 60m = 140m.