Question

The sum of two numbers is 16. The sum of their reciprocals is 1/3. Find the numbers.

Answer 1

Let the numbers be ‘a’ and ‘b’ 

Given, sum of two numbers is 16. The sum of their reciprocals is 1/3. 

⇒ a + b = 16 

⇒ a = 16 – b 

Also, 1/a + 1/b = 1/3 

⇒ 1/(16 – b) + 1/b = 1/3 

⇒ 3(b + 16 – b) = 16b - b² 

⇒ b² – 16b + 48 = 0 

⇒ b² – 12b – 4b + 48 = 0 

⇒ b(b – 12) – 4(b – 12) = 0 

⇒ (b – 4)(b – 12) = 0 

⇒ b = 4, 12 

Numbers are 4 , 12