Question

8. The sum of the numerator and the denominator of a fraction is 9. If one is added to the numerator and one is subtracted from the denominator, it reduces to 1/2 Find the fraction. ​

Answer 1

To find : fraction

Given : The sum of the numerator and the denominator of a fraction is 9.

Solution :

• Let, numerator be $x$ and denominator be $y$ .
• Then as per given data , we have following conditions :

1. $x + y = 9$

       $x =9 - y$

    2. $\frac{x + 1}{y -1 } = \frac{1}{2}$

• Now, substituting the value of $x$ in condition 2. we get ,

       $\frac{9- y + 1}{y - 1} = \frac{1}{2}$

• On solving we get ,

          $2 ( 10-y) = y - 1 \\20- 2y = y-1$

                    $21 =3y \\y =\frac{21}{3} \\y = 7$

• substituting value in 1. we get

                  $x = 9 - 7\\ = 2$  

• Therefore , fraction is

                 $\frac{x}{y} = \frac{2}{7}$

Hence , required fraction is $\frac{2}{7}$.