The running track of the park is 800 metres in circumference. Mayank and Aman start from the same point and walk in opposite directions at 5 km/hr and 6 km/hr respectively.

Consider the following statements:

Statement I: They will meet for the first time after 4 minutes and 22 seconds.
Statement II: By the time they meet, Aman would have covered 440 metres.

Select the correct answer from below:

(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both statements I and II are correct.
(d) None of the statements is correct.

Question

The running track of the park is 800 metres in circumference. Mayank and Aman start from the same point and walk in opposite directions at 5 km/hr and 6 km/hr respectively.

Consider the following statements:

Statement I: They will meet for the first time after 4 minutes and 22 seconds.
Statement II: By the time they meet, Aman would have covered 440 metres.

Select the correct answer from below:

(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both statements I and II are correct.
(d) None of the statements is correct.

ONLiNE UPSC · Accepted Answer

Circumference of the track = 800 metres
Mayank's speed = 5 km/hr = (5 &times; 1000) / 3600 = 25/18 m/s
Aman's speed = 6 km/hr = (6 &times; 1000) / 3600 = 5/3 m/s
Since they walk in opposite directions, their relative speed = 25/18 + 5/3 = 55/18 m/s
Time to meet = Distance / Relative Speed = 800 / (55/18) = (800 &times; 18) / 55 = 14400 / 55 &asymp; 261.82 seconds
Convert to minutes: 261.82 seconds &asymp; 4 minutes and 22 seconds
Statement I: Correct

Distance covered by Aman = Speed &times; Time = (5/3) &times; 261.82 &asymp; 436.37 metres
Statement II: Incorrect (as it says 440 metres)

So, option (a) is correct.

Time, Speed and Distance

Relative Speed

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