Question 56

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.

Solution

Let 'a' and 'b' be the speeds of Rahim and the speed boat in still water, respectively

Let 'c' be the speed of the stream.

Speed boat starts after 1 minute of Rahim's departure and crosses him after 4 minutes.

It implies that the speed boat covered the same distance in 4 minutes that Rahim took 5 minutes.

Hence, the ratio of upstream speeds of Rahim and Speed boat = $$\frac{a-c}{b-c}=\frac{4}{5}$$

Using Statement 1, we get $$b=30\ kmph$$. But, it's not sufficient to get the value of 'a'.

Using Statement 2, we get $$a-c=\frac{30}{3}=10\ kmph$$. But it's also not sufficient to get the value of 'a'.

using both statements, we get

$$\ \frac{\ a-c\ }{b-c}=\frac{4}{5}$$

$$\ \frac{\ 10\ }{30-c}=\frac{4}{5}$$

$$\ \ 50\ =120-4c$$

$$\ \ c\ =17.5$$

$$\ \ a=17.5+10=27.5\ kmph$$


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