Question

The total time by the boat to cover 72 km upstream and 180 km downstream in 16 hours. The total time taken by the same boat to cover 108 km upstream and 126 downstream in 16 hours. If the sum of the upstream speed and downstream speed of the boat is 30 km, then find the speed of the stream.

• A. 2 kmph
• B. 5 kmph
• C. 3 kmph
• D. 4 kmph

Answer 1

Answer:

C. 3 kmph

Explanation: 

Downstream speed = d kmph

Upstream = u kmph

$\frac{72}{u}+\frac{180}{d} = 16$…… (1)

$\frac{108}{u} +\frac{126}{d} = 16$ …… (2)

Equate both the equation (1) and (2)

$\frac{72}{u} + \frac{180}{d} = \frac{108}{u} + \frac{126}{d}$

$\frac{54}{d} = \frac{36}{u}$

$\frac{d}{u} = \frac{54}{36}$

$\frac{d}{u} = \frac{3}{2}$

Downstream speed = $\frac{3}{5}\times{30}$ = 18 kmph

Upstream speed = $\frac{2}{5}\times{30}$ = 12 kmph

The speed of the stream = $\frac{(18-12)}{2} = \frac{6}{2}$ = 3 kmph