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.

Explanation

Let the fraction be `(x)/(y)`, where numerator is x denominator is y.
According to I condition, `(x + 2)/(y) = (1)/(2)`
implies 2x + 4 = y
implies 2x - y = - 4 …(1)
According to II condition, `(x)/(y-1) = (1)/(3)`
implies 3x = y - 1
implies 3x - y = - 1 ...(2)
Subtracting equation (2) from (1), we get
-x = - 3
implies x = 3
Substituting x = 3 in equation (1), we get
`2 xx 3 - y = - 4`
implies - y = - 10
implies y = 10
Hence, the required fraction is `(x)/(y) = (3)/(10)`.