Question

The sum of two numbers is 15. If the sum of their reciprocal is 3/10 Find smallest number.

• A. $5$
• B. $10$
• C. $7$
• D. $8$

Answer 1

The correct option is A $5$

Let first number =$x$
then the other number = $15-x$
According to the question
$\frac{1}{x}+\frac{1}{15-x}=\frac{3}{10}$
$10(15-x+x)=3\left(x(15-x)\right)$
$150=45x-3x^2$
$3x^2-45x+150=0$
$x^2-15x+50=0$
$x^2-10x-5x+50=0$
$(x-10)(x-5)=0$
$x=10,x=5$