A bus starts from a bus stop P and goes to another bus stop Q In between P and Q there is a bridge A...........

Quant (SSC) Time & distance

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?

Bus travels 3x times faster than the man

Bus travels 2x times faster than the man

The bus and the man travel at the same speed

4x the speed of the man is equal to 3x the speed of the bus

छोटे Courses बड़े Results

Master Time & distance

Prepare through Micro-courses

Try Now

Explanation:

Let the speed of the bus be ‘b’ and man be ‘m’.
Let the distance between P and A be y.
AC:CB = 1:3 implies AC = x and CB = 3x
When bus goes from P to A and the man from C to A, time taken by both are equal and they meet at A.
y/b = x/m or
b/m = y/x --- (1)
When bus goes from P to B and the man from C to B, again time taken by both are equal and they meet at B.
(y+x+3x)/b = 3x/m
b/m = (4x+y)/3x ---(2)
Equating (1) and (2), we get y/x = (4x+y)/3x
3y = 4x + y or y = 2x
Therefore ratio of speeds b/m = 2x/x or 2 : 1
The Bus travels 2x times faster than the man.

Report error

Submit Error