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A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

a) 4 km/hr
b) 5 km/hr
c) 6 km/hr
d) 10 km/hr

Answer: b
Explanation: Let the speed of the stream be x km/hr
Speed downstream = (15 + x) km/hr
Speed upstream = (15 – x) km/hr
$$\eqalign{ & \frac{{30}}{{ {15 + x} }} + \frac{{30}}{{ {15 – x} }} = 4\frac{1}{2} \cr & \frac{{900}}{{225 – {x^2}}} = \frac{9}{2} \cr & 9{x^2} = 225 \cr & {x^2} = 25 \cr & x = 5\,km/hr \cr} $$

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