A boat goes 40 km upstream and 50 km downstream in 10 hours. It goes 15 km upstream in 25 km downstream in 4 hours. The speed of the current?

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answer is C.

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Detailed Solution

Speed of the boat = x km/hr

Speed of the current = y km/hr

$\begin{array}{l} \frac{40}{x - y} + \frac{50}{x + y} = 10 \to (1) \\ \frac{15}{x - y} + \frac{25}{x + y} = 4 \to (2) \\ \frac{1}{x - y} = u, \frac{1}{x + y} = v \\ 40 u + 50 v = 10 \Rightarrow 40 u + 50 v = 10 \\ 15 u + 25 v = 4 - 30 u - 50 v = 8 \\ 10 u = 2 \\ u = \frac{1}{5} \Rightarrow v = \frac{1}{25} \\ u = \frac{1}{5} \Rightarrow \frac{1}{5} = \frac{1}{x - y} \\ x - y = 5 x - y = 5 \\ x + y = 25 15 - y = 5 \\ 2 x - 30 y = 10 \\ x = 15 \\ S p e e d o f c u r r e n t = (y) = 10 k m /hr \end{array}$