Question

The denominator of a fraction is greater than its numerator by 11.If 8 is added to both its numerator and denominator,it becomes $\frac{3}{4}$.Find the fraction.

Answer 1

Given: The denominator of a fraction is greater than its numerator by 11. If 8 is added to both its numerator & denominator, it becomes 3/4.

To find : the fraction.

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

Now acccording to the question,
The denominator of a fraction is greater than its numerator by 11.
$\to$ y = x + 11 ......... (1)

If 8 is added to both its numerator & denominator, it becomes 3/4.
$\to$ $\frac{x+8}{y+8}$ =$\frac{3}{4}$

$\to$ 4(x+8) = 3 (y +8)

$\to$ 4x +32 = 3y + 24

$\to$ 4x - 3y = -32 +24

$\to$ 4x - 3y = -8 ......... (2)

Now substituting y from eq (1) to eq (2) , we get

$\to$ 4x -3 ( x+ 11) = -8

$\to$ 4x -3x-33 = -8

$\to$ x = -8 +33

$\to$ x = 25
now
$\to$ y= x+ 11
$\to$ y = 25+11 = 36
Therefore the fraction which is =$\frac{x}{y}$ = $\frac{25}{36}$

The required fraction is $\frac{25}{36}$