Multiple choice

The question is followed by two statements, I and II. Mark the answer as per the given conditions. [CAT 2003 – Leaked] If A and B run a race, then A wins by 60 seconds. If B and C run the same race, then B wins by 30 seconds. Assuming that C maintains a uniform speed what is the time taken by C to finish the race? I. A and C run the same race and A wins by 375 metres. II. The length of the race is 1 km.

  1. statement I alone is required to answer the question, but not statement II.

  2. statement II alone is required to answer the question, but not statement I.

  3. both statements I and II together are needed to answer the question.

  4. cannot be answered even with the help of both the statements together.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The first condition gives C's finishing time as A's finishing time plus 90 seconds. Statement I relates A's speed and the race length through the 375 m margin, while statement II supplies the race length of 1000 m. Neither statement alone determines C's time, but together they do.

AI explanation

Let the length of the race be L and the speeds of A, B, and C be a, b, and c, and from the prompt we know A beats B by 60 seconds and B beats C by 30 seconds, meaning A beats C by 90 seconds. Statement II gives the length of the race L as 1 km or 1000 m. Statement I provides the winning margin of A over C as 375 m, meaning when A finishes 1000 m, C has run 625 m, so the ratio of their speeds a to c is 4 to 5. This means C takes 5 fourths of the time A takes to finish the race, and since A beats C by 90 seconds, if time taken by A is t, then 5t fourths minus t equals 90 seconds, yielding t equals 360 seconds, making the total time for C equal to 450 seconds. Since statement II provides the race length and statement I provides the speed ratio of A to C, both are required together to solve the problem.

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