Question

The sum of 2 numbers is 18. If the sum of their reciprocals is `1/4` , find the numbers. 

Answer 1

Let these numbers be A and B. 

Then as per the question, 

A+B= 18, 1/ A + 1/ B= l / 4 

⇒  A= 18-B, Putting this in 2nd equation, we get: 

⇒ `1/(18 - "B") + 1/"B" = 1/4`

⇒ (B + 18 - B) × 4 = (18 - B) × B

⇒ B² -18 B + 72 = 0 

⇒ B² -12 B - 6 B + 72 = 0 

⇒ B(B-12)- 6(B-12) = 0 

⇒ (B-12)(B-6) = 0 

⇒ B= 12, 6. 

Hence the numbers are 6 and 12.