Question

13. The sum of the numerator and denominator of a certain fraction is 10. If 1 is subtracted for 2 both the numerator and denominator, the fraction is decreased by 21 Find the fraction​

Answer 1

Suppose the fraction is

y

x

If 1 is added to the numerator and 1 is subtracted to the denominator the fraction becomes 1

y−1

x+1

=1

x+1=y−1

x−y=−2 Equation (1)

If 1 is added to the denominator the fraction becomes half

y+1

x

=

2

1

2x=y+1

2x−y=1 Equation (2)

On subtracting Equation 1 from 2 we get

2x−y−x+y=1+2

x=3

Substituting the value of x in equation 1 we get,

3−y=−2

y=5

y

x

=

5

3

Numerator is 3.