Question

The sum of two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.

Answer 1

Let one of the number be x then other number is (18 - x).

Then according to question,

`1/x+1/(18-x)=1/4`

`rArr(18 - x+x)/(x(18-x))=1/4`

⇒ 18 x 4 = 18x - x²

⇒ 72 = 18x - x²

⇒ x² - 18x + 72 = 0

⇒ x² -12x - 6x + 72 = 0

⇒ x(x - 12) - 6(x - 12) = 0

⇒ (x - 6)(x - 12) = 0

⇒ x - 6 = 0

⇒ x = 6

Or

⇒ x - 12 = 0

⇒ x = 12

Since, x being a number,

Therefore,

When x = 12 then another number will be

18 - x = 18 - 12 = 6

And when x = 6 then another number will be

18 - x = 18 - 6 = 12

Thus, the two numbers are 6 and 12.