Question

sum of the numerator and denominator of a fraction is 19 .if 2 is added to the denominator the new fraction formed is 1/2 .find the original fraction?

Answer 1

Answer : Let the numerator of the fraction be x and the denominator on the fraction is y

Therefore the fraction is x/y.

According to first condition :

x + y = 19 - equation 1

According to second condition :

x/y+2=1/2

Cross multiplying we get :

2x=y+2

2x-y=2 - equation 2

x+y =19 -from equation 1

2x-y=2-from equation 2

Cancel positive and negative y

And add x and 2x and 19 and 2

Therefore 3x =21

x = 21 /3

x = 7

Put x=7 in equation 1

x + y = 19

7 + y = 19

y = 19 - 7

y = 12

Therefore the original fraction is 7/12.

Step-by-step explanation: