Question

A fraction becomes ¼ if 2 is subtracted from the numerator and 3 added to the denominator . If 6 is added to the numerator and the denominator is multiplied by 3, it becomes 2/3 . find the fraction

Answer 1

SOLUTION :-

Let,

Numerator = x

Denominator = y

According to the first condition,

$\longrightarrow\sf \dfrac{x-2}{y+3}=\dfrac{1}{4} \\\\\longrightarrow 4(x-2) = y+3 \\\\\longrightarrow 4x-8 = y+3 \\\\\longrightarrow 4x-y = 11 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...........................(1)$

According to the second condition,

$\longrightarrow\sf \dfrac{x+6}{3y}=\dfrac{2}{3} \\\\\longrightarrow 3(x+6) = 2\times 3y \\\\\longrightarrow 3x+18 = 6y \\\\\longrightarrow 3x - 6y = - 18 \\\\\longrightarrow x- 2y = - 6 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...........................(2)$

Eq (1) × 2,

$\longrightarrow\sf 8x-2y = 22 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...........................(3)$

Eq (3) - Eq (2),

$\longrightarrow\sf 7x = 28\\\\\longrightarrow\bf x = 4$

Substitute the value of x in eq (1),

$\longrightarrow \sf 4\times 4 -y = 11 \\\\\longrightarrow 16-y = 11 \\\\\longrightarrow -y = -5 \\\\\longrightarrow\bf y = 5$

$\bf FRACTION = \dfrac{4}{5}$