Question

A fraction becomes `(1)/(3)` when 2 is subtracted from the numerator and it becomes `(1)/(2)` when 1 is subtracted from the denominator. Find the fraction.

Answer 1

Let’s assume the fraction be `x/y`

1st condition:

`(x - 2)/y = (1)/(3)`

⇒ 3x – 6 = y

⇒ 3x – y = 6   ...(1)

2nd condition:

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

⇒ 2x – y – 1

⇒ 2x – y = –1

Using elimination method:

Multiplying (2) by –1 and then adding (1) and (2)

⇒ 3x – y = 6

⇒ –2x + y = 1

⇒ x = 7

Now, from (1)

⇒ 3x – y = 6

⇒ 3(7) – y = 6

⇒ 21 – y = 6

⇒ y = 15

Hence, the required fraction is `(7)/(15)`.