Question

Find a fraction which becomes `(1/2)` when 1 is subtracted from the numerator and 2 is added to the denominator, and the fraction becomes `(1/3)` when 7 is subtracted from the numerator and 2 is subtracted from the denominator.

Answer 1

Let the required fraction be `x/y`.

Then, we have:

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

⇒ 2(x – 1) = 1(y + 2)

⇒ 2x – 2 = y + 2

⇒ 2x – y = 4   ...(i)

Again,`(x - 7)/(y - 2) = 1/3`

⇒ 3(x – 7) = 1(y – 2)

⇒ 3x – 21 = y – 2

⇒ 3x – y = 19   ...(ii)

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

x = (19 – 4)

x = 15

On substituting x = 15 in (i), we get:

2 × 15 – y = 4

⇒ 30 – y = 4

⇒ y = 26

∴ x = 15 and y = 26

Hence, the required fraction is `15/26`.