A and B are two points on a straight line. Ram runs from A to B while Rahim runs from B to A. After crossing each other, Ram and Rahim reach their destinations in one minutes and four minutes, respectively. If they start at the same time, then the ratio of Ram's speed to Rahim's speed is

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10 months ago

Question :

A and B are two points on a straight line. Ram runs from A to B while Rahim runs from B to A. After crossing each other, Ram and Rahim reach their destinations in one minutes and four minutes, respectively. If they start at the same time, then the ratio of Ram's speed to Rahim's speed is

A.
2
B.
√2
C.
1/2
D.
2√2

Option A is the correct answer.

Explanatory Answer

Assuming Ram’s speed = ‘a’ and Rahim’s speed = ‘b’.
If they cross each other at time ‘t’:
Distance travelled by Ram = a*t
Distance travelled by Rahim = b*t
Further time taken by Ram to reach B = (Dist. Remaining/Speed) = (b*t)/a = 1min -------①
Similarly, further time taken by Rahim to reach A = (a*t)/b = 4min -------②
Assume ratio (a/b) = x
Therefore, ① becomes: t/x = 1 &
② becomes: t*x = 4
Multiplying both equations, we get: t 2 = 4
Therefore t = 2
Applying value of t, we get x = 2 = a/b