Question

a fraction becomes 1/3 when 1 is added to the numerator and it becomes 1/4 when 8 is added to the 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 :-

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

Eq (2) - Eq (1) :-

$\longrightarrow \bf x = 11$

Substitute the value of x in eq (1) :-

$\longrightarrow \sf 3 \times 11 - y = - 3 \\\\\longrightarrow 33 - y =- 3 \\\\\longrightarrow -y = -36 \\\\\longrightarrow\bf y = 36$

$\bf FRACTION = \dfrac{11}{36}$