Question

Ramu went by car from Calcutta to Trivandrum via Madras, without any stoppages. The average speed 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.

• A. if the question can be answered with the help of statement I alone
• B. if the question can be answered with the help of statement II alone
• C. if both statement I and statement II are needed to answer the question
• D. if the statement cannot be answered even with the help of both the statements

Hint:

Average speed over different segments requires both distance and speed ratio information for each part of the journey.

Answer 1

The Correct Option is C

Let the distance from Calcutta to Madras be $d$ km, and average speed for this part be $v_1$ kmph. Let the distance from Madras to Trivandrum be $0.3d$ km, and speed be $v_2$ kmph.
From Statement I alone: We know the ratio of distances but have no information on speed, so we cannot find $v_2$.
From Statement II alone: We know $v_2 = 2v_1$, but without distance ratio, we cannot find exact values.
Combining both: Using weighted harmonic mean for average speed, $(d + 0.3d)/(d/v_1 + 0.3d/v_2) = 40$. Substituting $v_2 = 2v_1$ allows solving for $v_1$, then finding $v_2$. Thus, both statements together are sufficient.