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A motor boat, whose speed is $20 km / hr$ in still water takes 1 hour more to go 48 km

upstream than to return downstream to the same spot. Find the speed of the stream.

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4 km / hr

5 km / hr

6 km / hr

7 km / hr

answer is A.

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Detailed Solution

Suppose stream speed = x km/hr
Boat speed in the still water =20 km/hr
So, the boat speed with downstream

= 20 + x km / hr

Also, the boat speed of boat with upstream,

= 20 - x km / hr

We know that,
Time= distance/time.
Since, Total distance is 48 km and the difference of time taken is 1 hour. So,

\frac{48}{20 - x} - \frac{48}{20 + x} = 1

48 [\frac{1}{20 - x} - \frac{1}{20 + x}] = 1

[\frac{20 + x - 20 + x}{(20 - x) (20 + x)}] = \frac{1}{48}

\frac{2 x}{400 - x^{2}} = \frac{1}{48}

96 x = 400 - x^{2}

x^{2} + 96 x - 400 = 0

x^{2} + 100 x - 4 x - 400

x (x + 100) - 4 (x + 100) = 0

(x - 4) (x + 100) = 0

x = 4 or x = - 100

Neglect negative value.
Thus, speed of the stream = 4 km/hr.
Correct option is 1.

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