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

• Quadratic Equations (C10)

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

Answer

Let two parts be x and 27 – x

∴ 1/x + 1/(27 – x) = 3/20

⇒ x² – 27x + 150 = 0

⇒ (x – 15) (x – 12) = 0

⇒ x = 12 or 15

∴ The two parts are 12 and 15.