Question

The numerator of a fraction is 3 less than the denominator. When both the numerator and denominator are increased by 4, the fraction is increased by fraction $\frac{12}{77}$. Find the original fraction.

• A. $\frac{4}{7}$
• B. $\frac{3}{7}$
• C. $\frac{4}{5}$
• D. None of these

Answer 1

The correct option is A $\frac{4}{7}$

Let the fraction be x /x+3

$\Rightarrow \frac{x+4}{x+7}=\frac{12}{77}+\frac{x}{x+3}$

$\Rightarrow \frac{x+4}{x+7}=\frac{89x+36}{77(x+3)}$

$\Rightarrow 77(x^2+7x+12)=89x^2+89.7x+36x+36.7$

$\Rightarrow 12x^2+120x-672=0$

$\Rightarrow x^2+10x-56=0$

$\Rightarrow (x+14)(x-4)=0$

$\Rightarrow x=4$ as x can not be negative

$\therefore$the fraction is $\frac{4}{7}$