Question

A number is decreased by 50%, and the result is increased by 50% to get99. What is the original number? *

Answer 1

Let the original number be

$=x$

The number decreased by 50% means that we will first calculate 50% of the original number and then subtract it from the original number x

$\begin{gathered} 50\text{ \% of the original number will give} \\ =50\text{ \% of x} \\ =\frac{50}{100}\times x=0.5x \end{gathered}$

Then, let's subtract the decreased value from the original value

The remaining value will be

$\begin{gathered} \text{remaining value} \\ =x-0.5x \\ =0.5x \end{gathered}$

The result is increased by 50% to get

$\begin{gathered} increasedvalue=50\text{ \% of the remaining value} \\ =\frac{50}{100}\times0.5x \\ =0.5\times0.5x \\ =0.25x \end{gathered}$

The new value after increasing by 50 % can be gotten by adding the increased value to the remaining value

$\begin{gathered} \text{the new value will be} \\ =0.5x+0.25x \\ =0.75x \end{gathered}$

From the question, the new value =99

Therefore, the original value will be

$\begin{gathered} 0.75x=99 \\ \text{divide both sides by 0.75} \\ \frac{0.75x}{0,75}=\frac{99}{0.75} \\ x=132 \end{gathered}$

Hence,

The original number = 132