Question

The sum of the numerator and denominator of a fraction is 2 more than twice the numerator. If the numerator and the denominator are reduced by 3, they are in the ratio 3 : 4. Find the fraction.

Answer 1

Let the numerator be x and the denominator be y,

According to the given conditions:

(i) The sum of the numerator and the denominator is 2 more than twice the numerator:

x + y = 2x + 2

y = 2x − x +2

y = x + 2     ...(1)

(ii) When both are reduced by 3, they are in the ratio 3 : 4:

`(x - 3)/(y - 3) = 3/4`

4(x − 3) = 3(y − 3)

4x − 12 = 3y − 9

4x − 3y = 12 − 9

4x − 3y = 3     ...(2)

Substitute equation (1) into (2):

4x − 3(x + 2) = 3

4x − 3x − 6 = 3

x − 6 = 3

x = 3 + 6

∴ x = 9

Now, substitute x = 9 into equation (1):

y = x + 2

y = 9 + 2

∴ y = 11

Hence, the fraction is `9/11`.