A, B and C are situated on the bank of a rive | vedclass

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Question

(D) Let $d$ be the distance between $A$ and $B$,and $B$ and $C$. Let $x$ be the speed of the swimmer in still water and $y$ be the speed of the stream

Vedclass · Accepted Answer

$5:1$

Vedclass · Answer

(D) Let $d$ be the distance between $A$ and $B$,and $B$ and $C$. Let $x$ be the speed of the swimmer in still water and $y$ be the speed of the stream.For the round trip between $A$ and $B$: $\frac{d}{x+y} + \frac{d}{x-y} = 10 \dots (1)$For the downstream trip from $A$ to $C$ (total distance $2d$): $\frac{2d}{x+y} = 8 \Rightarrow d = 4(x+y) \dots (2)$Substitute $d$ from $(2)$ into $(1)$:$\frac{4(x+y)}{x+y} + \frac{4(x+y)}{x-y} = 10$$4 + \frac{4(x+y)}{x-y} = 10$$\frac{4(x+y)}{x-y} = 6 \Rightarrow \frac{x+y}{x-y} = \frac{6}{4} = \frac{3}{2}$$2(x+y) = 3(x-y)$$2x + 2y = 3x - 3y$$x = 5y$Therefore,the ratio $\frac{x}{y} = \frac{5}{1}$.

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