Question

The denominator of a fraction is 9 more than its numerator. If the numerator and denominator both are increased by 7. The new fraction becomes 7/10. Find the original fraction

Answer 1

let initially numerator is x and denominator is y
then y=x+9
now if 7 is added both to the numerator and denominator then fraction becomes
(x+7)/(y+7)=(7/10)
(x+7)/(x+16)=(7/10)
10x+70=7x+96
3x=26
x=(26/3)
y=(26/3)+9
y=(26+27)/3
y=53/3
therefore original fraction is
x/y=(26/3)/(53/3)
=26/53

Answer 2

Given:

The denominator of a fraction is 9 more than its numerator. If the numerator and denominator both are increased by 7. The new fraction becomes 7/10.

To find:

We have to find the original fraction.

Solution:

The denominator of a fraction is 9 more than its numerator.

Thus let the fraction is x/(x+9).

If the numerator and denominator both are increased by 7 then the fraction becomes-

$\frac{x + 7}{x + 9 + 7} \\ = \frac{x + 7}{x + 16}$

The new fraction becomes 7/10.

So, we can write-

$\frac{x + 7}{x + 16} = \frac{7}{10} \\ 10x + 70 = 7x + 112 \\ 3x = 42 \\ x = 14$

The fraction is-

$\frac{14}{14 + 9} \\ = \frac{14}{23}$

The original fraction is 14/23.