The sum of two numbers is 15. The sum of their reciprocals is $\frac{5}{18}$. Find the numbers.

The correct option is B

9 and 6

Let the numbers be $x$ and $15-x$

$\frac{1}{x}+\frac{1}{15-x}=\frac{5}{18}$

$\frac{15}{x(15-x)}=\frac{5}{18}$

$54=15x-x^2$

$x^2-15x+54=0$

$x^2-9x-6x+54=0$

$(x-9)(x-6)=0$

x = 9, 6

Taking $x$ = 9, $15-x$ = 6

Taking $x$ = 6, $15-x$ = 9

Hence, two numbers are 9 and 6.