Question

Denominator of a Fraction exceeds its numeration by 6 . If 1 is added to the

numerator and 3 is substracted from the denominater, the new friction is

$\frac{3}{4}$ . find the orignal fraction.

Answer 1

Let the numerator be x and denominator be y.'So the fraction is $\frac{x}{y}$

$y=x+6$

$\frac{x+1}{y-3}$ $=$ $\frac{3}{4}$

Substituting $y=x+6$ in the above equation,

$\frac{x+1}{x+6-3}$ $=$ $\frac{3}{4}$

$\frac{x+1}{x+3}$ $=$ $\frac{3}{4}$

Cross multiplying,

$4x+4=3x+9$

$x=5$

$y=x+6$

$y=11$
$\therefore fraction=\frac{x}{y}=\frac{5}{11}$