Question

The denominator of a fraction exceeds its numerator by 8. If 1 is added to the numerator and 4 is subtracted from the denominator the fraction becomes 4/7 find the original fraction?​

Answer 1

Answer

As we know that,

The denominator is greater than numerator by 8. So,

Let the numerator be y.

Let the denominator be y + 8.

${\sf \dashrightarrow \dfrac{Numerator}{Denominator} = \dfrac{y}{y + 8}}$

Numerator of the fraction :

According to the question,

${\sf \dashrightarrow \dfrac{y + 1}{y + 8) - 4} = \dfrac{4}{7}}$

Cross multiply the numbers.

${\sf \dashrightarrow 7 (y + 1) = 4 (y + 8 - 4)}$

${\sf \dashrightarrow 7y + 7 = 4y + 32 - 16}$

${\sf \dashrightarrow 7y - 4y = 32 - 16 - 7}$

${\sf \dashrightarrow 7y - 4y = 16 - 7}$

${\sf \dashrightarrow 3y = 9}$

${\sf \dashrightarrow y = \dfrac{9}{3}}$

${\sf \dashrightarrow y = 3}$

Denominator of the fraction :

${\sf \dashrightarrow y + 8 = 3 + 8}$

${\sf \dashrightarrow 11}$

So, the original fraction is

${\sf \dashrightarrow \dfrac{3}{11}}$

Hence, the original fraction is ${\sf \dfrac{3}{11}}$.