Multiple choice

Passage

[CAT 2000] Directions for Questions 5 and 6: There are five machines A, B, C, D and E situated on a straight line at distances of 10 metres, 20 metres, 30 metres, 40 metres and 50 metres 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 material is 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 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.

Suppose on a certain day, machines A and D have sent the first two messages to the origin at the beginning of the first second, and C has sent a message at the beginning of the 5th second and B at the beginning of the 6th second, and E at the beginning of the 10th second. How much distance in metres 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 metres per second.

  1. 140

  2. 80

  3. 340

  4. 360
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A Correct answer
Explanation

The robot serves machines in order of distance. At t=0, A(10m) and D(40m) are waiting. Robot travels to D (40m) and back (40m), total 80m. At t=5, C(30m) is waiting. Robot travels to C(30m) and back(30m), total 60m. Total distance = 80 + 60 = 140m. The robot notices E at the origin after returning from C.

AI explanation

The robot starts at the origin and receives messages from A and D at the first second, so it immediately travels to D covering 40 m and then returns 40 m to the origin, which at 10 m per second takes 8 seconds, bringing the total time to 9 seconds. During this trip, messages from C and B arrived at 5 and 6 seconds, but they were pending at the station until the robot returned, so the robot immediately travels to the furthest pending machine which is C at 30 m, serving A along the way, and then returns to the origin, adding 60 m to the distance and taking another 6 seconds to bring the time to 15 seconds. The message from E at 10 seconds is still waiting at the origin when the robot arrives, and the question asks for the distance travelled when it first notices this message of E, meaning the distance covered up to that exact moment of return to the station. The total distance travelled is the initial 80 m plus the 60 m from the second trip, equaling 140 m, confirming the robot has travelled 140 m when it arrives back and notices the pending message from E.

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