The sum of the numerator and denominator of a fraction is 8. If 3 is a

1.	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 \(\frac{3}4\) . Find the fraction.
Answer» 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 .

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 \(\frac{3}4\) . Find the fraction.

Answer»

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 .