Question

The sum of reciprocals of two number is $\frac{11}{30}$ and difference of reciprocals of two is $\frac{-1}{30}$. Find the two numbers.

• A. 5 & 6
• B. 3 & 2
• C. 7 & 9
• D. 11 & 13

Answer 1

The correct option is A 5 & 6

Given, Let the numbers be $x\&y$
Reciprocal $\Rightarrow \frac{1}{x}\&\frac{1}{y}$

$\frac{1}{x}+\frac{1}{y}=\frac{11}{30}\frac{1}{x}-\frac{1}{y}=\frac{-1}{30}$
Consider, $a=\frac{1}{x};b=\frac{1}{y}$
$a+b=\frac{11}{30}---\left(i\right)a-b=\frac{-1}{30}---\left(ii\right)$

Add $\left(i\right)\&\left(ii\right)$
$a+b=\frac{11}{30}\underset{–}{a-b=\frac{-1}{30}}2a=\frac{11}{30}-\frac{1}{30}=\frac{10}{30}=\frac{1}{3}\therefore a=\frac{1}{6}$

Substitute value of $a$ in $\left(i\right)$
$\frac{1}{6}+b=\frac{11}{30}b=\frac{11}{30}-\frac{1}{6}=\frac{11-5}{30}=\frac{6}{30}=\frac{1}{5}$

Now, $x=\frac{1}{a}=6\&y=\frac{1}{b}=5$

The numbers are $5\&6$