CAT Quantitative Aptitude Questions | CAT Time Speed and Distance & Races

The question is from the topic relative speed. It discusses about the relative speed between a bus and a man. Time Speed and Distance is a favorite part in CAT Exam, and appears more often than expected in the CAT Quantitative Aptitude section in the CAT Exam

Question 15 :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?

1. Bus travels 3x times faster than the man
2. Bus travels 2x times faster than the man
3. The bus and the man travel at the same speed
4. 4x the speed of the man is equal to 3x the speed of the bus

Explanatory Answer

Method of solving this CAT Question from Time Speed Distance: Think about the time taken by the bus and the man! That will tell you what their speeds are related to!

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 question is "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?"

Hence, the Bus travels 2x times faster than the man.

Choice B is the correct answer.