Question

When 3 is subtracted from the numerator of a fraction it becomes ⅓ and if 11 is subtracted from the the denominator it becomes ½. Find the fraction ​

Answer 1

SOLUTION :-

Let,

Numerator = x

Denominator = y

According to the first condition,

$\longrightarrow\sf \dfrac{x-3}{y}= \dfrac{1}{3} \\\\\longrightarrow 3(x-3) = y \\\\\longrightarrow 3x-9=y\\\\\longrightarrow 3x-y=9 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \..............(1)$

According to the second condition,

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

Equation (1) - Equation (2),

$\longrightarrow\bf x= 20$

Substitute the value of x in equation (1),

$\longrightarrow \sf 3\times 20-y= 9 \\\\\longrightarrow 60-y = 9 \\\\\longrightarrow -y = -51\\\\\longrightarrow\bf y = 51$

$\bf FRACTION = \dfrac{20}{51}$