Question

The speed of a river is 5 kmph. How long will it take to reach a point that is 11 km upstream?
Statement 1: Relative speed is 8 kmph
Statement 2: Speed of the man in still water is 6 kmph

• A. If the data in statement (1) alone is sufficient to answer the question
• B. If the data in statement (2) alone is sufficient to answer the question
• C. If the data in both the statements together are needed to answer the question
• D. If either statement (1) alone or statement (2) alone is sufficient to answer the question

Hint:

Upstream speed equals still-water speed minus river speed; each statement gives one of these speeds directly or indirectly.

Answer 1

The Correct Option is D

Step 1: Understand upstream travel.
Going upstream means moving against the current, so the effective speed relative to the ground is (speed in still water) minus (speed of the river). The river's speed is 5 kmph, the distance to cover is 11 km, and time = distance divided by this effective (relative) speed.

Step 2: Check statement (1) alone.
Statement (1) directly gives the relative speed while going upstream as 8 kmph. Time taken is \[ \text{Time}=\frac{\text{Distance}}{\text{Relative speed}}=\frac{11}{8}\text{ hours} \] This is one fixed number, so statement (1) alone answers the question completely.

Step 3: Check statement (2) alone.
Statement (2) gives the man's speed in still water as 6 kmph. The upstream speed is then \(6-5=1\) kmph (still water speed minus river speed). Time taken is \[ \text{Time}=\frac{11}{1}=11\text{ hours} \] This too is one fixed number, using only statement (2).

Step 4: Final answer.
Statement (1) alone gives the time as \(\frac{11}{8}\) hours, and statement (2) alone gives it as 11 hours; either one, taken by itself, is enough to compute a definite time. \[ \boxed{\text{Either statement alone is sufficient}} \]