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

CAT Questions | Time and distance | Races

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. 9/10th 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

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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}\\)

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

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

Choice A is the correct answer.

 

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