XAT 2023 — QA & DI Question 17
The problem below consists of a question and two statements numbered 1 & 2. You have to decide whether the data provided in the statements are sufficient to answer the question.
Rahim is riding upstream on a boat, from point A to B, at a constant speed. The distance from A to B is 30 km. One minute after Rahim leaves from point A, a speedboat starts from point A to go to point B. It crosses Rahim’s boat after 4 minutes. If the speed of the speedboat is constant from A to B, what is Rahim’s speed in still water?
1. The speed of the speedboat in still water is 30 km/hour.
2. Rahim takes three hours to reach point B from point A.
Answer & solution
- A
Statement 1 alone is sufficient to answer the question, but statement 2 alone is not sufficient
- B
Statement 2 alone is sufficient to answer the question, but statement 1 alone is not sufficient
- C
Each statement alone is sufficient
Both statements together are sufficient, but neither of them alone is sufficient
- E
Statements 1 & 2 together are not sufficient
Let the speed of river be 'r' kmph.
Rahim and Speedboat start from A and meet at a point M (say).
Going upstream, Rahim takes 5 minutes to cover this distance while Speedboat takes 4 minutes to cover the same distance.
∴ = ...(1)
We need to find SRahim
Statement (1): SSpeedboat = 30
If we put SSpeedboat = 30 in (1), this alone would not be sufficient to calculate SRahim.
∴ Statement (1) alone is not sufficient to answer the question.
Statement (2): Rahim takes 3 hours to reach B.
⇒ SRahim - r = 30/3 = 10 kmph.
Since we don't know the value of r, we cannot determine the SRahim.
∴ Statement (2) alone is not sufficient to answer the question.
Using both statements together we have, SSpeedboat = 30 kmph and SRahim - r = 10 kmph.
Putting these values in (1), we get
=
⇒ r = 17.5 kmph.
⇒ SRahim - 17.5 = 10
⇒ SRahim - 17.5 = 27.5 kmph
∴ Using both statements we can get the answer.
Hence, option (d).