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.
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.
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.
Show Hint
Track the robot trip by trip: a message sent while the robot is away is noticed only when it gets back to the origin.
Updated On: Nov 4, 2026
- 340
- 80
- 140
- 360
Show Solution
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The Correct Option is C
Solution and Explanation
Step 1: Trip 1.
At the very start (time 0) A and D have sent messages, so the robot leaves at once. It goes to D (40 m), serving A on the way, and returns to the origin: \(2\times40=80\) m, taking 8 s. It is back at \(t=8\) s.
Step 2: Messages received meanwhile.
C (sent at the beginning of the 5th second, \(t=4\)) and B (6th second, \(t=5\)) were sent while the robot was away, so it notices them on returning at \(t=8\). E's message is sent at the beginning of the 10th second (\(t=9\)), which is after the robot has left again.
Step 3: Trip 2.
The robot goes to C (30 m), serving B on the way, and returns: \(2\times30=60\) m, taking 6 s. It is back at \(t=14\) s. E's message (sent at \(t=9\)) arrived while it was away, so it is noticed only now.
Step 4: Total distance.
\(80+60=140\) m.
Final Answer:
The correct option is (3): 140
At the very start (time 0) A and D have sent messages, so the robot leaves at once. It goes to D (40 m), serving A on the way, and returns to the origin: \(2\times40=80\) m, taking 8 s. It is back at \(t=8\) s.
Step 2: Messages received meanwhile.
C (sent at the beginning of the 5th second, \(t=4\)) and B (6th second, \(t=5\)) were sent while the robot was away, so it notices them on returning at \(t=8\). E's message is sent at the beginning of the 10th second (\(t=9\)), which is after the robot has left again.
Step 3: Trip 2.
The robot goes to C (30 m), serving B on the way, and returns: \(2\times30=60\) m, taking 6 s. It is back at \(t=14\) s. E's message (sent at \(t=9\)) arrived while it was away, so it is noticed only now.
Step 4: Total distance.
\(80+60=140\) m.
Final Answer:
The correct option is (3): 140
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