Question

Two times a number is a $100\%$ increase in the number. If we take half the number what would be the decrease in percent ?

Answer 1

Let the number be $x$.

Therefore, twice the number $=2\times x=2x$ and

Number obtained after $100\%$ increase in the number $=x+x\times 100\%$

$=x+x\times \frac{100}{100}$

$=x+x$

$=2x$

Hence, the given statement is true and is valid for any number $x$.

Now, half of the number $x=\frac{x}{2}$

Hence, decrease $\%=\frac{\text{Decrease in amount}}{\text{Original amount}}\times 100\%$

$=\frac{\frac{x}{2}}{x}\times 100\%$

$=\frac{100\%}{2}$

$=50\%$

Hence, decrease in percent is $50\%$.