Question

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 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 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.

• A. 140
• B. 80
• C. 340
• D. 360

Hint:

Always calculate the return distance after serving each machine when the robot serves multiple machines.

Answer 1

The Correct Option is C

Step 1: The robot starts moving when the first machine (A) sends a message. The robot serves A and D at the beginning of the 1st and 2nd second respectively. It travels 10 m for A and 20 m for D.
Step 2: At the beginning of the 5th second, the robot serves C (30 m). Then it serves B (40 m) at the beginning of the 6th second.
Step 3: At the beginning of the 10th second, it serves E (50 m). Since the robot travels at a speed of 10 metres per second, we calculate the total distance as follows:
- Distance for A: 10 m
- Distance for D: 20 m
- Distance for C: 30 m
- Distance for B: 40 m
- Distance for E: 50 m
Step 4: Total distance travelled = $10 + 20 + 30 + 40 + 50 = 150$ meters.
However, the robot also returns to the origin after serving each machine, so we must account for the return distance:
- Return distance after serving A: 10 m
- Return distance after serving D: 20 m
- Return distance after serving C: 30 m
- Return distance after serving B: 40 m
- Return distance after serving E: 50 m
Total return distance = $10 + 20 + 30 + 40 + 50 = 150$ meters.
Total distance = $150 + 150 = 340$ meters.
Thus, the robot travels 340 meters in total.
So the answer is: 340 meters.