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

CAT Questions

The question is from the topic races. The question is about a race between three persons and their respective speeds. Time Speed and Distance is a favorite in CAT Exam, and appears more often than expected in the CAT Quantitative Aptitude section in the CAT Exam

Question 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. 9/10^th of Antony's speed
2. 5/8^th of Akbar's speed
3. 14/15^th of Antony's speed
4. 10/7^th of Akbar's speed

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Explanatory Answer

Method of solving this CAT Question from Races:Compare Amar's and Antony's speeds at 2 instances - when Antony completes and when Akbar completes!

When Antony completes, Amar would have run (x – 14) m; Time taken is the same
Ratio of Amar’s speed : Antony’s speed = \\frac{x-14}{t1}\\) : \\frac{x}{t1}\\) or \\frac{x-14}{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 = \\frac{x-32}{t2}\\) : \\frac{x-20}{t2}\\) or \\frac{x-32}{x-20}\\) ---- (2)
Equating (1) and (2), we get
\\frac{x-14}{x}\\) = \\frac{x-32}{x-20}\\)
x² – 34x + 280 = x² – 32x
2x = 280
Or x = 140 m
Ratio of Amar’s speed : Antony’s speed = \\frac{(140-14)}{140}\\) = \\frac{126}{140}\\) = \\frac{9}{10}\\)

Alternate & intutive Approach:
When Akbar finishes the race, Antony is 20m away from the finish line and Amar is 32m away
When Antony finishes the race, Amar is 14m away from the finish line

This implies that in the same time Antony and Amar covered 20m and 32-14 = 18m respectively...
So the speeds of Antony and Amar will be in the ratio 20 : 18 or 10 : 9
That means, Amar's speed 9/10^th of Antony's speed.

Answer Suggestion by : Sarbeswar Behera, Student of 2IIM.

The question is "What is Amar’s speed?"

Hence, Amar's Speed is 9/10^th of Antony's Speed

Choice A is the correct answer.