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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
Bus travels 3x times faster than the man
CORRECT ANSWER WRONG ANSWER
B
Bus travels 2x times faster than the man
CORRECT ANSWER WRONG ANSWER
C
The bus and the man travel at the same speed
CORRECT ANSWER WRONG ANSWER
D
4x the speed of the man is equal to 3x the speed of the bus
CORRECT ANSWER WRONG ANSWER
Solution

Correct option is

(B)

Explanatory Answer :

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