CAT Practice : Speed Time, Races

Think about the time taken by the bus and the man! That will tell you what their speeds are related to!

Ratio of Speeds

    Q.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

 

  • Correct Answer
    Choice B. Bus travels 2x times faster than the man

Detailed Solution



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

Correct Answer: Bus travels 2x times faster than the man



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More questions from Speed Time, Races

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"Life is a race ... if you don't run fast ... you will be like a broken undaa" - Veerusahasra Buddhi