A fraction becomes frac{1}{4} if 2 is subtrac | vedclass

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(A) Let the numerator of the fraction be $x$ and the denominator be $y$.According to the first condition,if $2$ is subtracted from the numerator and $

Vedclass · Accepted Answer

$\frac{4}{5}$

Vedclass · Answer

(A) Let the numerator of the fraction be $x$ and the denominator be $y$.According to the first condition,if $2$ is subtracted from the numerator and $3$ is added to the denominator,the fraction becomes $\frac{1}{4}$.$\frac{x-2}{y+3} = \frac{1}{4}$$4(x-2) = y+3$$4x - 8 = y + 3$$4x - y = 11$ .......... $(1)$According to the second condition,if $6$ is added to the numerator and the denominator is multiplied by $3$,the fraction becomes $\frac{2}{3}$.$\frac{x+6}{3y} = \frac{2}{3}$$3(x+6) = 2(3y)$$3x + 18 = 6y$$3x - 6y = -18$Dividing by $3$,we get $x - 2y = -6$ .......... $(2)$From equation $(1)$,$y = 4x - 11$. Substituting this into equation $(2)$:$x - 2(4x - 11) = -6$$x - 8x + 22 = -6$$-7x = -28$$x = 4$Now,substitute $x = 4$ into $y = 4x - 11$:$y = 4(4) - 11 = 16 - 11 = 5$Therefore,the original fraction is $\frac{x}{y} = \frac{4}{5}$.

$A$ fraction becomes $\frac{1}{4}$ if $2$ is subtracted from the numerator and $3$ is added to the denominator. If $6$ is added to the numerator and the denominator is multiplied by $3$,it becomes $\frac{2}{3}$. Find the fraction.

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