Question

The sum of two numbers is $15$. If the sum of their reciprocal is $\left(\frac{3}{10}\right)$, then find the numbers.

Answer 1

Let one of the numbers be $x$.

Since, sum of the numbers is 15, the other number will become $(15-x)$

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

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

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

$\frac{15}{(15x-x^2)}=\frac{3}{10}$

$150=45x-3x^2$

$3x^2-45x+150=0$ (taking $3$ common )

$x^2-15x+50=0$

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

$x=10$ or $5$

Therefore, the numbers are $10$ and $5$.