# 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

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 = ${{(x – 14) \over t1}}$ : ${{x \over t1}}$
Or ${{(x – 14) \over x}}$ ---- (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 = ${{(x – 32) \over t2}}$ : ${{(x - 20) \over t2}}$
Or ${{(x – 32) \over (x - 20)}}$ ---- (2)

Equating (1) and (2), we get
${{(x – 14) \over x}}$ = ${{(x – 32) \over (x - 20)}}$
x2 – 34x + 280 = x2 – 32x
2x = 280
Or x = 140 m

Ratio of Amar’s speed : Antony’s speed = ${{(140 – 14) \over 140}}$ = ${{126 \over 140}}$ = ${{9 \over 10}}$

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

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## More questions from Speed Time, Races

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