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) = 5 

∴ x = 3 and y = 5 

Hence, the required fraction is 3/5 .