Question

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

Answer 1

Let the two parts be x and (27 - x)

According to the given condition, 

`1/x+1/(27-x)=3/20` 

⇒ `(27-x+x)/(x(27-x))=3/20` 

⇒ `27/(27x-x^2)=3/20` 

⇒ 27x - x² = 180 

⇒ x² - 27x + 180 = 0 

⇒ x² - 15x - 12x + 180 = 0 

⇒ x(x - 15) - 12(x - 15) = 0 

⇒ (x - 12)(x - 15) = 0 

⇒ x - 12 = 0 or x - 15 = 0 

⇒ x = 12 or x = 15 

When x = 12, 

27 - x = 27 - 12 = 15 

When x = 15 

27 - x = 27 - 15 = 12 

Hence, the required parts are 15 and 12.