Question

Divide 27 into two parts such that sum of their reciprocals is 3 by 20

Answer 1

solving the equation you will get x=15 or 12 which is the answer.

Answer 2

Let number = x

Another number = 27 - x

According to question;

1/x + 1/(27 - x) = 3/20

(27 - x + x)/(27x - x²) = 3/20

Cross-multiply,

20(27) = 3(27x - x²)

540 = 81M - 3x²

x² - 27x + 180 = 0

x² - 15x - 12x + 180 = 0

x(x - 15) -12(x - 15) = 0

(x - 12) (x - 15) = 0

x = 12, 15