Divide 27 into two parts such that the sum of their reciprocals is `3/20`

Answer

12 and 15

Explanation

`(1)/(x)+(1)/((27-x))=(3)/(20)implies(27-x+x)/(x(27-x))=(3)/(20)impliesx^(2)-27x+180=0`
`impliesx^(2)-15x-12x+180=0.`