Question

the denominator of a fraction is greater than numerator by 8 if the numerator is increased by 17 and denominator is decreased by 1, the number obtained is 3/2 find the fraction.

Answer 1

this is an important question for class 8

Answer 2

Solution :-

Let :-

Numerator = x

Denominator = y

According to the first condition :-

$\longrightarrow \sf y = x+8 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ......................(1)$

According to the second condition :-

$\longrightarrow \sf \dfrac{x+17}{y-1} = \dfrac{3}{2} \\\\\longrightarrow 2(x+17)= 3(y-1) \\\\\longrightarrow 2x+34 = 3y-3 \\\\\longrightarrow 2x-3y = -37 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ......................(2)$

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

$\longrightarrow \sf 2x- 3(x+8) = -37 \\\\\longrightarrow 2x-3x-24 = -37 \\\\\longrightarrow -x = -13 \\\\\longrightarrow \bf x = 13$

Substitute x = 13 in eq (1) :-

$\longrightarrow \sf y = 13+8\\\\\longrightarrow \bf y = 21$

$\bf FRACTION = \dfrac{13}{21}$