Question

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.

• 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
• D. Both statements together are sufficient, but neither of them alone is sufficient
• E. Statements 1 & 2 together are not sufficient

Answer 1

The Correct Option is D

Let the speeds be: \[ \text{Rahim’s speed} = R \ \text{kmph}, \quad \text{Speedboat (still water)} = S \ \text{kmph}, \quad \text{Stream speed} = W \ \text{kmph}. \] They cross each other at point \(X\).

From given conditions: \[ \frac{AX}{R - W} = \frac{5}{60}, \quad \frac{AX}{S - W} = \frac{4}{60}. \] Eliminating \(AX\): \[ W = 5R - 4S \quad \ldots (1) \]

Statement I: \(S = 30 \ \text{kmph}\). Since \(W\) or \(AX\) is not known, Statement I alone is not sufficient.

Statement II: \[ \frac{BA}{R + W} = \frac{3}{60} \ \text{hours}, \quad \text{or simply speed } (R+W)=3 \ \text{km/hr}. \] Since \(S\) or \(AX\) is not known, Statement II alone is not sufficient.

Combining I and II:
Substituting \(S = 30\) in (1): \[ W = 5R - 4(30) = 5R - 120 \] From Statement II: \[ R + W = 10 \quad \Rightarrow \quad W = 10 - R. \] Equating: \[ 10 - R = 5R - 120 \] \[ 6R = 130 \quad \Rightarrow \quad R = \tfrac{65}{3}. \]

Final Answer:
Both statements together are sufficient. Hence, the correct option is: \[ \boxed{D} \]