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The speed of a boat in still water is $15 km / h$ . It goes $30 km$ upstream and returns back at the same point in 4 hour 30 minutes, then the speed of stream is,

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2 km/hr

3km/hr

4km/hr

5km/hr

answer is D.

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Detailed Solution

Given that,
The speed of a boat in still water is

15 km / h

. It goes

30 km

upstream and returns back at the same point in 4 hour 30 minutes.
We know that,

Time = \frac{Distance}{Speed}

Let the speed of the stream is x

k m / h

then the time taken will be

30 x

.
Then,
Speed of the boat upstream=

(15 - x) km / h

.
Speed of the boat downstream=

(15 + x) km / h

.
So,
Time taken for upstream

= \frac{30}{15 - x}

hour.
Time taken for downstream

= \frac{30}{15 + x}

hour.
Given that total time

=

4 hour 30 minute.
Since, 1hour

=

60 minute. Then,
4 hour 30 minute

= 4 \frac{30}{60} hour = \frac{4}{2}

hour
According to the question,

30 15 − x + 30 15 + x = 92 ⇒ 30 15 + x + 30 15 − x 15 − x 15 + x = 92 ⇒ 900 225 − x 2 = 92 ⇒ x 2 − 25 = 0

We know that,

a^{2} - b^{2} = (a + b) (a - b)

Then,

⇒ x + 5 x − 5 = 0 ⇒ x = 5, x = − 5

The negative value of x is not possible because speed cannot be negative.
The speed of the stream is 5

k m / h

.
Hence, option 4 is correct.

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