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CAT 2004 — QA Question 26

Time, Speed & DistanceEasy
Passage / Data

Answer the following question based on the information given below.

In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks.

A sprinter starts running on a circular path of radius r metres. Her average speed (in metres/minute) is πr during the first 30 seconds, πr/2 during next one minute, πr/4 during next 2 minutes, πr/8 during next 4 minutes, and so on. What is the ratio of the time taken for the nth round to that for the previous round?

Answer & solution

  • A

    4

  • B

    8

  • 16

  • D

    32

Solution

Let πr = x.

∴ The circumference of the circular path = 2x.

∴ The sprinter covers 2x metres in one round. The time taken to complete each round is as under:

​​​​​​​

Thus, we see that the ratio of time taken for the second round to that for the 1st round = 16.

Similarly, ratio of time taken for the third round to that for the 2nd round = 16 and so on.

Hence, option (c).

CAT 2004 QA Q26: A sprinter starts running on a circular path of radius r metres. Her average speed (in metres/minute) is πr — Solution | TheCATExam