Question

A fraction become 1/3 when 1 is subtraction 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 to 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),

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

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