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

Let the two numbers be x and y.

According to the question,

x + y = 16 …(i)

…(ii)

Eq. (ii) can be re - written as

…(iii)

On putting the value of x + y = 16 in Eq. (iii), we get

xy = 48

On putting the value of in Eq. (i), we get

⇒ 48 + y² = 16y

⇒ y² – 16y + 48 = 0

⇒ y² – 12y – 4y + 48 = 0

⇒ y(y – 12) – 4(y – 12) = 0

⇒ (y – 4)(y – 12) = 0

⇒ y = 4 and 12

Hence, the two numbers are 4 and 12.