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)`

⇒ `3"x "- 6 = "y"`

⇒ `3"x" - "y" = 6`   ...(1)

2nd condition:

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

⇒ `2"x" - "y" - 1`

⇒ `2"x" - "y" = -1`

Using elimination method:
Multiplying (2) by -1 and then adding (1) and (2)

⇒ `3"x" - "y" = 6`
⇒  `-2"x" + "y" =1`
⇒ `"x" = 7`

Now, from (1)
⇒ `3"x" - "y" = 6`
⇒ `3 (7) - "y" = 6`
⇒ `21 - "y" = 6`
⇒ `"y" = 15`

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