Multiple choice

The question is followed by two statements, I and II. Mark the answer as per the given conditions. [CAT 1990] Ramu went by car from Calcutta to Trivandrum via Madras, without any stoppages. The average speeds for the entire journey was 40 kmph. What was the average speed from Madras to Trivandrum? I. The distance from Madras to Trivandrum is 0.30 times the distance from Calcutta to Madras. II. The average speed from Madras to Trivandrum was twice that of the average speed from Calcutta to Madras.

  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. can be answered by both statements independently.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let d1, d2 be distances and v1, v2 be speeds. We have total distance D = d1 + d2 and total time T = d1/v1 + d2/v2 = D/40. Statement I gives d2 = 0.3d1. Statement II gives v2 = 2v1. With two equations and variables, we can solve for the ratio of speeds or specific values.

AI explanation

Let the distance from Calcutta to Madras be d1 and the speed be v1, and let the distance from Madras to Trivandrum be d2 and the speed be v2, where the total average speed is 40 kmph for the total distance d1 plus d2. Statement I gives d2 equals 0.3 times d1, which we substitute into the average speed equation to get 40 equals d1 plus 0.3d1 divided by the quantity of d1 divided by v1 plus 0.3d1 divided by v2, which simplifies to 1.3 equals 0.025 multiplied by the quantity of v1 plus 0.3v2. Statement II provides the relation that v2 equals 2 times v1, and substituting this into the previous equation gives 1.3 equals 0.025 multiplied by the quantity of v1 plus 0.6v1, yielding v1 equals 40 kmph, which then allows us to calculate v2 as 80 kmph. Since both equations are required to find a unique numerical value for the average speed from Madras to Trivandrum, both statements together are needed.

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