The sum of any two natural numbers is 8. Find the numbers if the sum of their reciprocals is 8/15.

Let the natural numbers be a & b.

According to the question, a + b = 8 ...... (i)

Also,

⇒ 15(a + b) = 8ab

⇒ 15×8 = 8ab

⇒ ab = 15

Using (a – b)² = a² + b² – 2ab

⇒ (a – b)² = (a + b)² – 4ab

⇒ (a – b)² = 8² – 4×15

⇒ (a – b)² = 64 – 60

⇒ a – b = 4 ...... (ii)

Adding (i)&(ii)

⇒ 2a = 12

⇒ a = 6

⇒ b = 2.