Two friends $A$ and $B$ are $30 k m$ 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 $2 k m$ 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 $A$ ?

15

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Solution

The correct option is D $30$
Let the speed of $B$ $= x k m / h$
Then speed of $A$ $= 3 x k m / h$
Given $3 x + x = 2 k m / m i n$ $= 120 k m / h$
$4 x = 120$
$x = 30 k m / h$
Distance covered by them after $10 m i n$ $= 2 (10) = 20 k m$
Remaining distance $= 30 - 20 = 10 k m$
Time taken by $B$ to cover $10 k m =$ $\frac{10}{\frac{30}{60}} = 20 m i n$
Total time $= 10 + 20 = 30 m i n$
Hence, option D is correct.

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