Question 84

A man starts running from point P at 11:00 a.m. with a speed of 10 km/hr. He runs for 2 hours and then takes a 1 hour rest. He continues this process till he is caught by another man who starts at 2:00 p.m. from point P and runs non-stop at a speed of 15 km/hr towards the first man. At what time (in p.m.) will the first man be caught?

Solution

Speed of first man = 10 km/hr

The manÂ runs for 2 hours and then takes a 1 hour rest, => Distance covered by him in 3 hours = $$2\times10=20$$ km

Speed of second man = 15 km/hr

Now, at 2:00 pm, the second man starts running and the first man is at a distance of 20 km

After 2 hours, at 4:00 pm, distance covered by first man = $$20$$ km and he will not move for another hour

and distance covered by second man = $$2\times15=30$$ km

=> Distance between them at 4:00 pm = $$30-20=10$$ km

Now, time taken to cover 10 km by second man = $$\frac{10}{15}=\frac{2}{3}$$ hours

= $$(\frac{2}{3}\times60)$$ minutes = $$40$$ minutes

$$\therefore$$ Total time taken to catch first man from 2:00 pm = 2 hr and 40 minutes

=> At 4:40 pmÂ the first man will be caught.

=> Ans - (B)

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