Question

sum of numerator and denominator in a fraction =10 , if numerator increased by 2 and denominator increased by 3 fraction becomes 1/2 , find the fraction​

Answer 1

The fraction is  $\frac{3}{7}$ .

Step-by-step explanation:

We are given that sum of numerator and denominator in a fraction = 10 , if numerator increased by 2 and denominator increased by 3 fraction becomes 1/2.

Let the numerator of the fraction be $x$

and the denominator of the fraction be $y$.

So, according to the question;

• First condition states that the sum of numerator and denominator in a fraction is 10, that means;

                               $x+y=10$  

                                $y=10-x$  ------------------- [Equation 1]

• Second condition states that if numerator increased by 2 and denominator increased by 3 fraction becomes 1/2, that means;

                       

                                     $\frac{x+2}{y+3}=\frac{1}{2}$

                              $2(x+2)=y+3$

                                 $2x+4=y+3$

                                $2x+4=10-x+3$      {using equation 1}

                                 $2x+4=13-x$

                                 $2x+x=13-4$

                                       $3x=9$

                                      $x=\frac{9}{3} =3$

Now, putting value of x in equation 1 we get;

                                      $y=10-x$

                                      $y=10-3=7$

So, the resulting fraction is  $\frac{x}{y} =\frac{3}{7}$ .