Question

How long did Mr. X take to cover 5000 km journey with 10 stopovers?
I. The $i^{th}$ stopover lasted $i^2$ minutes.
II. The average speed between any two stopovers was 66 kmph.

• 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:

In travel time problems with stops, you need both moving speed and stop durations to find total journey time.

Answer 1

The Correct Option is C

From Statement I: Knowing the duration of each stopover (sum of $i^2$ for $i=1$ to $10$ minutes) gives total stoppage time, but we have no travel time without speed data. Hence, insufficient.
From Statement II: Knowing average speed between stopovers gives travel time but not stoppage time, so we cannot find the total journey time. Hence, insufficient.
Combining both: We can compute total stoppage time from I: $1^2 + 2^2 + ... + 10^2 = \frac{10(10+1)(2 10 + 1)}{6} = 385$ minutes. Travel time from II: total distance $5000$ km at $66$ kmph = $\frac{5000}{66}$ hours. Adding stoppage time (converted to hours: $385/60$) to travel time yields total journey time. Hence, both statements are needed.