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Explanation:

Let the speed of the boat in still water and the speed of the river be x and y respectively.
And the distance between office and home be 'd'.

⇒ $\frac{d}{2x+y}$ + $\frac{d}{2x-y}$ = $\frac{1}{4}\left(\frac{d}{x+y}+\frac{d}{x-y}\right)$

⇒ $\frac{d\left(4x\right)}{4x^2-y^2}$ = $\frac{1}{4}\left(\frac{d\left(2x\right)}{x^2-y^2}\right)$

⇒ 8(x² – y²) = 4x² – y²

⇒ x²/y² = 7/4

⇒ x/y = √7/2

Hence, option (b).