Question

The sum of the numerator and denominator of a fraction is 4 more than twice the numerator. If the numerator and denominator are increased by 3, they are in the ratio 2 : 3. Determine the fraction.

Answer 1

Let the required fraction be `x/y`.

As per the question

x + y = 4 + 2x

⇒ y – x = 4   ...(i)

After changing the numerator and denominator

New numerator = x + 3

New denominator = y + 3

Therefore

`(x + 3)/(y + 3) = 2/3`

⇒ 3(x + 3) = 2(y + 3)

⇒ 3x + 9 = 2y + 6

⇒ 2y – 3x = 3   ...(ii)

Multiplying (i) by 3 and subtracting (ii), we get:

3y – 2y = 12 – 3

⇒ y = 9

Now, putting y = 9 in (i), we get:

9 – x = 4

⇒ x = 9 – 4

⇒ x = 5

Hence, the required fraction is `5/9`.