At his usual rowing speed kapil can travel 12 miles downstream in a certain riven in 6 h less than h...........

Quant (SSC) Boats and Streams

At his usual rowing speed, kapil can travel 12 miles downstream in a certain riven in 6 h less than he takes to travel the same distance upstream. But, if he could double his usual rowing speed for his 24 mile round trip, the downstream 12 miles would then take only 1 h less than the upstream 12 miles, what is the speed of the current in mile/h?

2 2/3 mile/h

3 2/3 mile/h

5 2/3 mile/h

7 2/3 mile/h

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Explanation:

Let speed of Kapil in still water = x
and speed of the current = y
∴ Speed upstream = (x – y)
Speed downstream = (x + y)
According to the question,
12 /(x – y) - 12 /(x + y) = 6
⇒ 6 (x² – y²) = 24y
⇒ x² – y² = 4y
⇒ x² = 4y + y² .................(i)
Again, 12 /(2x – y) - 12/(2x + y) = 1
⇒ 6x² – y² = 24y
⇒ x² = 24y + y² /4 ............(ii)
From Eqs. (i) and (ii) , we get
4y + y² = 24y + y²/4
⇒ 16y + 4y²
= 24y + y²
⇒ 3y² = 8y
⇒ y = 8/3 = 2 2/3 mile/h