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(C) Let the speed of the boat in still water be $x\, km/h$ and the speed of the stream be $y\, km/h$.The speed upstream is $(x-y)\, km/h$ and the spee

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$4$

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(C) Let the speed of the boat in still water be $x\, km/h$ and the speed of the stream be $y\, km/h$.The speed upstream is $(x-y)\, km/h$ and the speed downstream is $(x+y)\, km/h$.According to the given conditions:$\frac{25}{x-y} + \frac{39}{x+y} = 8$ $...(i)$$\frac{35}{x-y} + \frac{52}{x+y} = 11$ $...(ii)$Let $\frac{1}{x-y} = A$ and $\frac{1}{x+y} = B$.Then,$25A + 39B = 8$ $...(iii)$$35A + 52B = 11$ $...(iv)$To solve for $A$ and $B$,multiply equation $(iii)$ by $4$ and equation $(iv)$ by $3$:$100A + 156B = 32$ $...(v)$$105A + 156B = 33$ $...(vi)$Subtracting $(v)$ from $(vi)$:$5A = 1 \Rightarrow A = \frac{1}{5}$.Substituting $A = \frac{1}{5}$ in equation $(iii)$:$25(\frac{1}{5}) + 39B = 8$$5 + 39B = 8 \Rightarrow 39B = 3 \Rightarrow B = \frac{1}{13}$.Now,$x-y = 5$ and $x+y = 13$.Adding these two equations: $2x = 18 \Rightarrow x = 9$.Subtracting the first from the second: $2y = 8 \Rightarrow y = 4$.Thus,the speed of the stream is $4\, km/h$.

$A$ motorboat travelling at some speed can cover $25\, km$ upstream and $39\, km$ downstream in $8\, h$. At the same speed,it can travel $35\, km$ upstream and $52\, km$ downstream in $11\, h$. The speed of the stream is........$km/h$.

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