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 = 8 kmph

Statement (2): Speed of man in still water = 6 kmph

• A. If the data in statement (1) alone is sufficient to answer the question, but the data in statement (2) alone is not sufficient.
• B. If the data in statement (2) alone is sufficient to answer the question, but the data in statement (1) alone is not sufficient.
• 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.
• E. If the data in neither statement (1) nor statement (2) is sufficient to answer the question, and more data is needed.

Hint:

Time = distance / upstream speed. Statement 1 hands you the upstream speed directly; statement 2 lets you build it from still-water speed minus river speed.

Answer 1

The Correct Option is D

To find the time to cover 11 km upstream, we need the effective upstream speed (speed relative to the ground while moving against the current). Time = distance / upstream speed.

Statement (1): The relative speed, that is, the effective speed of the man with respect to the ground while going upstream, is given directly as 8 kmph. Time = \(\frac{11}{8}\) hours = 1 hour 22.5 minutes. This is a complete, computable answer, so statement (1) alone is sufficient.

Statement (2): The speed of the man in still water is 6 kmph, and we already know the river's speed is 5 kmph. Going upstream, the current works against the swimmer, so the effective speed = speed in still water - speed of river = \(6 - 5 = 1\) kmph. Time = \(\frac{11}{1} = 11\) hours. This is also a complete, computable answer, so statement (2) alone is sufficient too.

Since each statement independently lets us compute a definite travel time, either statement alone is sufficient to answer the question. The correct choice is option (4).