​The sum of two numbers is 15. If the sum of their reciprocals is $$\frac{3}{10}$$​ then find the two numbers?​

Correct option is B

Given:

Sum of two numbers = 15

Sum of their reciprocals = $$\frac{3}{10}$$

Solution:

The first number is 'x'

The second number is 'y'

Sum of the numbers: x + y = 15 ......(1)

Sum of their reciprocals: $$\frac{1}{x} + \frac{1}{y}$$​ = $$\frac{3}{10}$$  .....(2)​

From equation 1, we can express y in terms of x:

y = 15 - x

Substitute the value of y in equation 2:

$$\frac{1}{x} + \frac{1}{15-x}$$​​= $$\frac{3}{10}$$​

$$\frac{(15 - x + x)} { x(15 - x)}$$​= $$\frac{3}{10}$$​  .

150 = 45x - 3x²

3x² - 45x + 150 = 0

x² - 15x + 50 = 0

(x - 10)(x - 5) = 0

x = 10 or x = 5

Find the corresponding values of y:

If x = 10, then y = 15 - 10 = 5

If x = 5, then y = 15 - 5 = 10

Therefore, the two numbers are 5 and 10.

Option (b) is right answer.