Question

eliminatation method A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. find the fraction​

Answer 1

SOLUTION :-

Let,

Numerator = x

Denominator = y

According to the first condition,

$\longrightarrow\sf\dfrac{x-1}{y}=\dfrac{1}{3} \\\\\longrightarrow 3(x-1)= y \\\\\longrightarrow 3x-3 = y \\\\\longrightarrow 3x-y = 3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..............(1)$

According the second condition,

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

Eq (2) - Eq(1),

$\longrightarrow \bf x = 5$

Substitute the value of x in eq (1),

$\longrightarrow\sf 5\times 3 -y= 3 \\\\\longrightarrow 15-y = 3 \\\\\longrightarrow -y = -12 \\\\\longrightarrow\bf y = 12$

$\bf FRACTION = \dfrac{5}{12}$