CAT Practice : Speed Time, Races

Compare Amar's and Antony's speeds at 2 instances - when Antony completes and when Akbar completes!

Speed in a race

    Q.17: Amar, Akbar and Antony decide to have a 'x' m race. Antony completes the race 14 m ahead of Amar. Akbar finishes 20 m ahead of Antony and 32 m ahead of Amar. What is Amar’s speed?
    1. 9/10th of Antony's speed
    2. 5/8th of Akbar's speed
    3. 14/15th of Antony's speed
    4. 10/7th of Akbar's speed

 

  • Correct Answer
    Choice A. 9/10th of Antony's speed

Detailed Solution

When Antony completes, Amar would have run (x – 14) m; Time taken is the same
Ratio of Amar’s speed : Antony’s speed = :
Or ---- (1)

When Akbar finishes, Amar would have run (x – 32) m; Antony would have run (x – 20) m; Time taken is the same
At this point, the ratio of Amar’s speed : Antony’s speed = :
Or ---- (2)

Equating (1) and (2), we get
=
x2 – 34x + 280 = x2 – 32x
2x = 280
Or x = 140 m

Ratio of Amar’s speed : Antony’s speed = = =



Correct Answer: Amar's speed is 9/10th of Antony's speed



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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