Question

if 3 is added to the numerator of a fraction the value of fraction becomes 1 when 3 is added to the denominator of the fraction the value of fraction becomes 1/4 what is the value of fraction ​

Answer 1

Answer:

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Answer 2

Solution :-

Let :-

Numerator = x

Denominator = y

According to the first condition :-

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

According to the second condition :-

$\longrightarrow \sf \dfrac{x}{y+3} = \dfrac{1}{4} \\\\\longrightarrow 4x= y + 3 \\\\\longrightarrow 4x-y = 3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .........................(2)$

Equation (2) - Equation (1) :-

$\longrightarrow \sf 3x = 6 \\\\\longrightarrow \bf x = 2$

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

$\longrightarrow\sf 2 - y = - 3 \\\\\longrightarrow -y = - 5 \\\\\longrightarrow \bf y = 5$

$\bf FRACTION = \dfrac{2}{5}$