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Question

# A bus starts from a bus stop P and goes to another bus stop Q. In between P and Q, there is a bridge AB of certain length. A man is standing at a point C on the bridge such that AC:CB = 1:3. When the bus starts at P and if the man starts running towards A, he will meet the bus at A. But if he runs towards B, the bus will overtake him at B. Which of the following is true?

CAT 2021

A
B
C
D
##### 4x the speed of the man is equal to 3x the speed of the bus
Solution

Correct option is

(B)

Assume speed of Bus = b, and speed of man = m.

When the bus starts at P and if the man starts running towards A, he will meet the bus at A

y/b = x/m

y = xb/m.......(1)

if he runs towards B, the bus will overtake him at B

y + 4x/b = 3x/m

y + 4x = 3xb/m.......(2)

From (1) and (2)

y + 4x = 3y

y = 2x

y/b = x/m

2x/b = x/m

b/m = 2