Question

2 Sum of the numerator and the denominator of a fraction is 13. If 4 is added to the numerator and
10 is added to the denominator of the fraction it becomes 1/2.find the fraction​

Answer 1

Answer :

5/8

Solution :

Let the numerator be N and denominator be D so that the required fraction will be N/D .

According to the question ,

Sum of the numerator and the denominator of the required fraction is 13 .

Thus ,

N + D = 13 ----------(1)

Also ,

It is given that ,

If 4 is added to the numerator and 10 is added to the denominator of the fraction it becomes 1/2 .

Thus ,

=> (N + 4)/(D + 10) = 1/2

=> 2(N + 4) = D + 10

=> 2N + 8 = D + 10

=> 2N - D = 10 - 8

=> 2N - D = 2 -----------(2)

Adding eq-(1) and (2) , we get ;

=> N + D + 2N - D = 13 + 2

=> 3N = 15

=> N = 15/3

=> N = 5

Now ,

Putting N = 5 in eq-(1) , we get ;

=> N + D = 13

=> 5 + D = 13

=> D = 13 - 5

=> D = 8

Hence ,

The required fraction is N/D ie. 5/8 .