Question

# Two friends $$A$$ and $$B$$ are $$30$$ km apart and they start simultaneously on motorcycles to meet each other. The speed of $$A$$ is $$3$$ times that of $$B$$. The distance between them decreases at the rate of $$2$$ km per minute. Ten minutes after they start $$A's$$ vehicle breaks down and $$A$$ stops and waits for $$B$$ to arrive. After how much time (in minutes) A started riding, does B meet A ?

A
15
B
20
C
25
D
30

Solution

## The correct option is B $$20$$Let speed of $$B = V \, km/hr$$Let speed of $$A = 3V \, km/hr$$ Given $$4r = 2 \times 60 \, km/hr \Rightarrow V = 30 \, km/hr$$Distance covered by then after $$10 \, min. = 2 \times 10 = 20 \, km$$So, remaining distance $$= (30 - 20) \, km = 10 km$$Time taken by $$B$$ to cover $$\displaystyle 10 \, km = \frac {10} {30} = 20 \, min$$Mathematics

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