Question

the denominator of a fraction is greater than its numerator by 3 .it numerator is decreased by 2 and denominator is increased by 1 the resulting fraction becomes 1/3 find the fraction​

Answer 1

Solution :-

Let,

Numerator = x

Denominator = y

According to the first condition :-

$\longrightarrow \sf y = x + 3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .................(1)$

According to the second condition :-

$\longrightarrow \sf \dfrac{x-2}{y+1}=\dfrac{1}{3} \\\\\longrightarrow 3(x-2) = y+1 \\\\\longrightarrow 3x - 6 = y+1 \\\\\longrightarrow 3x-y = 7 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .................(2)$

Substitute the value of x in eq (2) :-

$\longrightarrow \sf 3x- (x+3) = 7 \\\\\longrightarrow 3x-x-3 = 7 \\\\\longrightarrow 2x = 10 \\\\\longrightarrow \bf x = 5$

Substitute x = 5 in eq (1) :-

$\longrightarrow \sf y = 5+3 \\\\\longrightarrow \bf y = 8$

$\bf FRACTION = \dfrac{5}{8}$