Question

The denominator of a fraction is greater than its numerator by 11. If 8 is added to both its numerator and denominator, it becomes `3/4`. Find the fraction.

Answer 1

Let the required fraction be `x/y`.

Then, we have:

y = x + 11

⇒ y – x = 11   ...(i)

Again, `(x + 8)/(y + 8) = 3/4`

⇒ 4(x + 8) = 3(y + 8)

⇒ 4x + 32 = 3y + 24

⇒ 4x – 3y = –8   ...(ii)

On multiplying (i) by 4, we get:

4y – 4x = 44

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

y = (–8 + 44)

y = 36

On substituting y = 36 in (i), we get:

36 – x = 11

⇒ x = (36 – 11)

⇒ x = 25

∴ x = 25 and y = 36

Hence, the required fraction is `25/36`.