A boat covers 24 km upstream and 36 km downstream in 6 hours while it covers 36 km upstream and...........

Quant (SSC) Boats and Streams

A boat covers 24 km upstream and 36 km downstream in 6 hours while it covers 36 km upstream and 24 km downstream in 6 1/2 hours. The velocity of the current is:

1 km/hr

1.5 km/hr

2 km/hr

2.5 km/hr

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Explanation:

Let the upstream = x kmph and rate downstream = y kmph.
Then, 24/x + 36/x = 6 .......i
and 36/x + 24/y = 13/2 .....ii
Adding (i) and (ii) we get:
= 60(1/x + 1/y) = 25/2
or 1/x + 1/y = 5/24 .........iii
Subtracting (i) and (ii), we get:
= 12(1/x - 1/y) = 1/2
or 1/x - 1/y = 1/24..........iv
Adding (iii) and (iv), we get 2/x = 6/24 or x = 8
So, 1/8 + 1/y = 5/24 ⇔ 1/y = (5/24 - 1/8) = 1/12 ⇔ y = 12
∴ Speed upstream = 8 kmph, Speed downstream = 12 kmph.
Hence, rate of current 1/2(12 - 8) kmph = 2 kmph