Question

The sum of the numerator and denominator of a fraction is 8. If 3 is added to both of the numerator and the denominator, the fraction becomes `3/4`. Find the fraction.

Answer 1

Let the required fraction be `x/y`.

Then, we have:

x + y = 8   ...(i)

And `(x + 3)/(y + 3) = 3/4`

⇒ 4(x + 3) = 3(y + 3)

⇒ 4x + 12 = 3y + 9

⇒ 4x – 3y = –3   ...(ii)

On multiplying (i) by 3, we get:

3x + 3y = 24

On adding (ii) and (iii), we get:

7x = 21

⇒ x = 3

On substituting x = 3 in (i), we get:

3 + y = 8

⇒ y = (8 – 3)

⇒ y = 5

∴ x = 3 and y = 5

Hence, the required fraction is `3/5`.