Question 80

Mona and Sonastart simultaneously from two towns, P and Q, towards Q and P respectively at 8:00 AM.R is a checkpost which is midway between P and Q. Both Mona and Sona turn back towards their respective starting points whenever they reach R and every time-they reach their starting points they turn back andreturn to R. If the speeds of Mona and Sonaare 45 km/h and60 km/h respectively and PQ = 24 km, when will they reach R at the same time?

Solution

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To reach R at the same moment for the first time, Sona has to gain one entire trip (Q-R, R-Q,Q-R) which is 36 km, over Mona.

Hence, the difference between distances covered by Mona and Sona in time T shall be 36 km.

This means, 60T - 45T = 36,

or T = 144 min, which is 10:24 am.

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