XAT 2023 Question Paper | Quantitative Aptitude and Data Interpretation

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Question 2 : 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.

Video Explanation

Explanatory Answer

Let the speed of Rahim in still water be ‘R’ kmph.
Let the speed of the Speed Boat in still water be ‘S’ kmph.
Let the speed of the stream be ‘a’ kmph.
“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.”

This means, when both of them were travelling upstream, the time taken by the Speed Boat and Rahim to reach the same point is 4 mins and 5 mins respectively. This means their speeds are in the ratio 5 : 4 when they travel upstream.
\( \frac { S - a } { R - a } = \frac { 5 } { 4 } \)
Statement 1: The speed of the speedboat in still water is 30 km/hour.
S = 30
\( \frac { 30 - a } { R - a } = \frac { 5 } { 4 } \)
This piece of information on its own doesn’t solve our problem.
Statement 2: Rahim takes three hours to reach point B from point A.
This means Rahim’s upstream speed is \( \frac { 30 } { 3 } = 10 \mathrm { kmph } \)
R - a = 10
\( \frac { S - a } { 10 } = \frac { 5 } { 4 } \)
This piece of information on its own doesn’t solve our problem.
But when we club both the statements…
\( \frac { 30 - a } { 10 } = \frac { 5 } { 4 } \)
\( 4 ( 30 - a ) = 50 \)
\( 120 - 4 a = 50 \)
\( a = 17.5 \)
WKT, R - a = 10
R - 17.5 = 10
R = 27.5 kmph
Technically, this question is not solvable… We are assuming that the Speed Boat crosses Rahim before he reaches point B. If the Speed Boat crosses Rahim after he reaches point B (that is, when he is stationary), we can’t say that the ratio of their upstream speeds is 5 : 4.

So, the question is a bit flawed. But, Hey, we’ll let it pass.

The answer is 'Both statements together are sufficient, but neither of them alone is sufficient'

Choice D is the correct answer.

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