Question

If you subtract $\frac{1}{2}$ from a number and multiply the result by $\frac{1}{2}$, you get $\frac{1}{8}$. What is the number?

• A. $\frac{3}{4}$
• B. $\frac{1}{6}$
• C. $\frac{7}{4}$
• D. $\frac{3}{5}$

Answer 1

The correct option is A $\frac{3}{4}$

Let the required number be $x$. Then,

$(x-\frac{1}{2})\times \frac{1}{2}=\frac{1}{8}$

$\Rightarrow x-\frac{1}{2}=\frac{1}{8}÷\frac{1}{2}$ ....[on dividing both sides by $\frac{1}{2}]$

$\Rightarrow x-\frac{1}{2}=\frac{1}{8}\times \frac{2}{1}$

$\Rightarrow x-\frac{1}{2}=\frac{1}{4}$

$\Rightarrow x-\frac{1}{2}+\frac{1}{2}=\frac{1}{4}+\frac{1}{2}$ .... [by adding $\frac{1}{2}$ on both sides]

$\Rightarrow x=\frac{1+2}{4}$ ...[on taking LCM]

$\Rightarrow x=\frac{3}{4}$

Thus, the required number is $\frac{3}{4}.$