The sum of two numbers is 9. The sum of their reciprocal is $$\frac{1}{2}$$ One of the number is:​

Correct option is B

Given:

We are given the following conditions:
 x + y = 9
 $$\frac{1}{x} + \frac{1}{y} = \frac{1}{2}$$​​

Solution:

​$$\frac{1}{x }+ \frac{1}{y} =\frac{ 1}{2} \\\ \\2y + 2x = xy$$​​
Now, from the first equation, we know that x + y = 9. So, we substitute it into the equation:
2(x + y) = xy
2(9) = xy
xy = 18
Now we have a system of equations:
x + y = 9 ............equation (i)
xy = 18  ............equation (ii)

​$$(x-y)^2 = (x+y)^2 - 4xy$$ 

$$(x -y)^2 = 81 - 4 \times 18$$ 

$$(x -y)^2 = 81 - 72$$ 

$$(x -y)^2 = 9$$ 

x - y = 3   ......... equation (iii) 

x + y  =  9 .........equation(i)

add equation (iii) and (i) 

2x = 12 

x = 6 

from equation (i)

6 + y  =  9 . 

y = 3 

According to the option one number is 6