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?
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?"
Choice B is the correct answer.
CAT® (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.
2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093