Question

A Fraction become 1/3 when 1 is subtacted numerator and it is become 1/4 when 8 is denometor find the fraction

Answer 1

Correct question :-

A fraction become 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to the denominator. Find the fraction.

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) ,

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

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