Question

The sum of two numbers is 15. It the sum of their reciprocal is $\frac{3}{10}$ then find the difference of the numbers

• A. 7
• B. 10
• C. 3
• D. 5

Answer 1

Answer: (D)

5

Let the two numbers be $a+b$

$a+b=15$ …………$\left(1\right)$ [given]

$\therefore \frac{1}{a}+\frac{1}{b}=\frac{3}{10}$ [given]

$\frac{b+a}{ab}=\frac{3}{10}$ ………..$\left(2\right)$

Substituting equation $\left(1\right)$ in equation $\left(2\right)$

$\therefore \frac{15}{ab}=\frac{3}{10}$

$\therefore ab=50$

Also, we know

$(a-b{)}^2=(a+b{)}^2-4ab$

$(a-b{)}^2=(15{)}^2-4\times 50$

$(a-b{)}^2=225-200$

$(a-b{)}^2=25$

Taking root on both sides

$a-b=5$

Difference of the numbers $=5$.