# The sum of two numbers is 15 and the sum of their reciprocal is 3/10. Find the numbers.

Let the 1st natural number be x.

And the 2nd natural number is (15 - x).

Sum of their reciprocals = 3/10

According to the Question,

⇒ 1/x + 1/(15 - x) = 3/10

⇒ 15/(15x - x²) = 3/10

⇒ 150 = 45x - 3x²

⇒ 3x² - 45x + 150 = 0

⇒ x² - 15x + 50 = 0

⇒ x² - 5x - 10x + 50 = 0

⇒ (x - 10) (x - 5) = 0

⇒ x - 10 = 0 or x - 5 = 0

⇒ x = 10, 5

When x = 10

1st number = x = 10

2nd number = 15 - x = 15 - 10 = 5

When x = 5

1st number = x = 5

2nd number = 15 - x = 15 - 5 = 10

Hence, the numbers are 10 and 5 or 5 and 10.

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