Question

The numerator of a fraction is $7$ less than its denominator. If the denominator is increased by $9$ and the numerator by $2$, the fraction becomes $\frac{2}{3}$. Find the fraction.

• A. $\frac{25}{33}$
• B. $\frac{33}{25}$
• C. $\frac{26}{33}$
• D. $\frac{33}{26}$

Answer 1

The correct option is C $\frac{26}{33}$

Let the numerator be $x$ and

the denominator be $y$

Given that numerator of a fraction is $7$ less than its denominator

Therefore, $x+7=y$ ------(1)

Given that if the denominator increased by $9$ and the numerator by $2$ then the fraction is $\frac{2}{3}$

Therefore, $\frac{x+2}{y+9}=\frac{2}{3}$

$⟹3x+6=2y+18$

$⟹3x-2y=12$

$⟹3x-2(x+7)=12$

$⟹x-14=12$

$⟹x=26$

$⟹y=26+7=33$ (from (1))

Therefore, the fraction is $\frac{26}{33}$