The sum of numerator and denominator of a fraction is 3 less than twice the denominator. If each of the numerator and denominator is decreased by 1, the fraction becomes 1/2 Find the fraction.

Explanation

Let the required fraction be `(x)/(y)`. Then,
` (x+ y ) = 2y- 3 rArr x - y = - 3 `
And , ` (x - 1 ) /( y - 1 ) = (1)/(2)rArr 2 x - 2 = y - 1 `
`" " rArr 2 x - y = 1 `
On substracting (i) from (ii), we get ` x= 4`.
Putting ` x= 4` in (i), we get ` y = x+ 3 = 4 + 3 = 7`
` therefore x = 4 and y = 7`
Hence, the required faction is ` ( 4)/(7)`