If the numerator of a fraction is multiplied by 2 and the denominator is reduced by 5 the fraction becomes 6/5. And, if the denominator is doubled and the numerator is increased by 8, the fraction becomes 2/5. Find the fraction.

Explanation

Let the required fraction be ` (x)/( y)`. Then,
`(2x )/( y - 5) = (6)/(5) rArr 10 x = 6 ( y - 5) `
` " " rArr 10 x - 6y = - 30 `
`" " rArr 5 x - 3y = - 15 " " ` … (i)
and ` (x + 8 )/( 2y ) = ( 2 ) /( 5) rArr 5 ( x + 8) = 4 y `
` " " rArr 5 x - 4y = - 40 " " `... (ii)
On subtracting (ii) from (i), we get `y = 25`
Putting ` y = 25 ` in (i), we get
` 5x - ( 3 xx 25) = - 15 rArr 5x - 75 = - 15 rArr 5 x = 60 rArr x = 12.`
` therefore x = 12 and y = 25 `
Hence, the required fraction is ` (12)/( 25)`