If a man rows 4 km downstream in 3 hours and 2 km upstream in 2 hours then how long will he take to ...........

Quant (SSC) Boats and Streams

If a man rows 4 km downstream in 3 hours and 2 km upstream in 2 hours then how long will he take to cover 8 km in stationary (still) water?

5 hours

9 hours

8 hours

none of these

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Explanation:

Distance covered in downstream = 4 km
Time taken in downstream = 3 hours.
Rate of downstream = distance / time = a = 4km / 3 hours = 4/3 km/hr.
Distance covered in upstream = 2 km
Time taken in upstream = 2 hours.
Rate of upstream = distance / time = b = 2 km / 2 hours = 1 km/hr.
Speed in still water = (a + b)/2 = (1/2)(4/3 + 1) km/hr
= (1/2)(4 + 3)/3 = 7/6 km/hr.
Time Taken to cover 8 km in still water = distance / speed = 8 x 6/7
= 48 / 7 = 7 hours (approximately).

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