Question

If 2 is added to the numerator of a fraction, it reduces to `(1/2) `and if 1 is subtracted from the denominator, it reduces to `(1/3)`. Find the fraction.

Answer 1

Let the required fraction be `x/y`.

Then, we have:

`(x + 2)/y = 1/2`

⇒ 2(x + 2) = y

⇒ 2x + 4 = y

⇒ 2x – y = –4   ...(i)

Again, `x/(y - 1) = 1/3`

⇒ 3x = 1(y – 1)

⇒ 3x – y = –1   ...(ii)

On subtracting (i) from (ii), we get:

x = (–1 + 4)

x = 3

On substituting x = 3 in (i), we get:

2 × 3 – y = –4

⇒ 6 – y = –4

⇒ y = (6 + 4)

⇒ y = 10

∴ x = 3 and y = 10

Hence, the required fraction is `3/10`.