At its usual rowing rate a boat can travel 18 km downstream in 4 hours less than it takes to travel ...........

Quant (SSC) Boats and Streams

At its usual rowing rate, a boat can travel 18 km downstream in 4 hours less than it takes to travel the same distance upstream. But if he the usual rowing rate for his 28-km round trip was 2/3rd, the downstream 14 km would then take 12 hours less than the upstream 14 km. What is the speed of the current?

1.5 km/h

3 km/h

2 km/h

3.5 km/h

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Explanation:

Let speed of boat = x km/hr, and of current = y km/hr
So
18/(x-y) = 18/(x+y) + 4
Gives x² = 9y + y²……..(1)
Now when speed of boat is 2x/3
14/(2x/3 -y) = 14/(2x/3 +y) + 12
42/(2x-3y) = 42/(2x+3y) + 12
Gives 4x² = 21y + 9y²…………(2)
From (1), put value of x² in (2) and solve
Solving, x = 6, y = 3
Hence, the speed of the current is 3 km/hr