Question

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

27 is divided into two parts such that the sum 3 of their reciprocals is `3/20`. Find the ratio between the numbers.

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 

If one number = 12, other number = 27 – 12 = 15

If one number = 15, other number = 27 – 15 = 12

Ratio = 12 : 15 = 4 : 5 or 15 : 12 = 5 : 4

Hence, the ratio of two numbers = 5 : 4.