Question

When $\frac{1}{3}$ is divided by the reciprocal of a particular number, the result is $8$ less than the number. Find the number.

• A. $3$
• B. $6$
• C. $8$
• D. $12$

Answer 1

Answer: (D)

$12$

Let the number be $x$
Reciprocal of $x$ is $\frac{1}{x}$.
As per problem, the equation can be written as
$\Rightarrow \frac{\frac{1}{3}}{\frac{1}{x}}=x-8$
$\Rightarrow \frac{1}{3}\times x=x-8$
$\Rightarrow \frac{x}{3}=x-8$
$\Rightarrow x=3x-24$
$\Rightarrow -2x=-24$
$\Rightarrow x=12$