The denominator of a fraction is greater than its numerator by 11. If

1.	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» 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) = 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 25/36 .

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»

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) = 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 25/36 .