10 yr before,the ratio of ages of A and B wa | vedclass

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(C) Let the ages of $A$ and $B$ $10 \ yr$ ago be $13x$ and $17x$ respectively.Their present ages are $(13x + 10)$ and $(17x + 10)$.After $17 \ yr$ fro

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$27$

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(C) Let the ages of $A$ and $B$ $10 \ yr$ ago be $13x$ and $17x$ respectively.Their present ages are $(13x + 10)$ and $(17x + 10)$.After $17 \ yr$ from now,their ages will be $(13x + 10 + 17)$ and $(17x + 10 + 17)$,which simplifies to $(13x + 27)$ and $(17x + 27)$.According to the problem,the ratio after $17 \ yr$ is $10: 11$:$\frac{13x + 27}{17x + 27} = \frac{10}{11}$$11(13x + 27) = 10(17x + 27)$$143x + 297 = 170x + 270$$297 - 270 = 170x - 143x$$27 = 27x$$x = 1$Therefore,the present age of $B = 17x + 10 = 17(1) + 10 = 27 \ yr$.

$10 \ yr$ before,the ratio of ages of $A$ and $B$ was $13: 17$. After $17 \ yr$ from now,the ratio of their ages will be $10: 11$. The present age of $B$ is (in $yr$):

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