# 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.

## Most Viewed Questions

### Preparation Products

##### Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
##### Knockout NEET Aug 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
##### Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
##### Knockout NEET Aug 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-