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 $\frac{3}{4}$. Find the fraction.

Answer 1

Let the required fraction be $\frac{x}{y}$.
Then, we have:
y = x + 11
⇒ y − x = 11 ....(i)
Again, $\frac{x+8}{y+8}=\frac{3}{4}$
⇒ 4(x + 8) =3(y + 8)
⇒ 4x + 32 = 3y + 24
⇒ 4x − 3y = −8 ....(ii)
On multiplying (i) by 4, we get:
4y − 4x = 44 ....(iii)
On adding (ii) and (iii), we get:
y = (−8 + 44) = 36
On substituting y = 36 in (i), we get:
36 − x = 11
⇒ x = (36 − 11) = 25
∴​ ​x = 25 and y = 36
Hence, the required fraction is $\frac{25}{36}$.