CAT 2017 [slot 1] Question with solution 07

Let the speed of the river be $x$ and the speed of the boat be $u$. Let $d$ be the one way distance and $t$ be the initial time taken.

Given,

$t = \frac{d}{u - x} + \frac{d}{u + x}$ ... i

Also,

$\frac{t}{4} = \frac{d}{2u - x} + \frac{d}{2u + x}$

$t = \frac{4d}{2u - x} + \frac{4d}{2u + x}$ ... ii

Equating both i and ii,

$\frac{d}{u - x}$+ $\frac{d}{u + x}$ = $\frac{4d}{2u - x} + \frac{4d}{2u + x}$

$\frac{2u}{u^2 - x^2} = \frac{16u}{4u^2 - x^2}$

$4u^2 - x^2 = 8u^2 - 8x^2$

$\frac{u^2}{x^2} = \frac{7}{4}$

$\frac{u}{x} = \frac{\sqrt{7}}{2}$