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} \\ =(50)/(100)* 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} \\ =(50)/(100)*0.5x \\ =0.5*0.5x \\ =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} \\ (0.75x)/(0,75)=(99)/(0.75) \\ x=132 \end{gathered}`

Hence,

The original number = 132