A fraction becomes frac{4}{5} if 1 is added t | vedclass

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Question

(C) Let the fraction be $\frac{x}{y}$.According to the first condition: $\frac{x+1}{y+1} = \frac{4}{5}$.Cross-multiplying gives: $5(x+1) = 4(y+1) \imp

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$\frac{7}{9}$

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(C) Let the fraction be $\frac{x}{y}$.According to the first condition: $\frac{x+1}{y+1} = \frac{4}{5}$.Cross-multiplying gives: $5(x+1) = 4(y+1) \implies 5x + 5 = 4y + 4 \implies 5x - 4y = -1$ (Equation $1$).According to the second condition: $\frac{x-5}{y-5} = \frac{1}{2}$.Cross-multiplying gives: $2(x-5) = 1(y-5) \implies 2x - 10 = y - 5 \implies 2x - y = 5$ (Equation $2$).From Equation $2$,$y = 2x - 5$. Substituting this into Equation $1$:$5x - 4(2x - 5) = -1$$5x - 8x + 20 = -1$$-3x = -21 \implies x = 7$.Now,find $y$: $y = 2(7) - 5 = 14 - 5 = 9$.Thus,the fraction is $\frac{7}{9}$.

$A$ fraction becomes $\frac{4}{5}$ if $1$ is added to both the numerator and the denominator. If $5$ is subtracted from both the numerator and the denominator,it becomes $\frac{1}{2}$. Find the fraction.

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