If i increase a number by 50 percent and then reduce it by 50 percent it will be 24 what is the original number

Answer 1

Let's denote the original number as $x$.

1. Increase by 50%: When you increase $x$ by 50%, you get: $$x+0.5x=1.5x$$

2. Reduce by 50%: Now, you take $1.5x$ and reduce it by 50%: $$1.5x-0.5(1.5x)=1.5x-0.75x=0.75x$$

According to the problem, this result is equal to 24: $$0.75x=24$$

3. Solve for $x$: To find $x$, divide both sides by 0.75: $$x=\frac{24}{0.75}$$

   Now, calculating $\frac{24}{0.75}$: $$x=24÷0.75=32$$

So, the original number is $\boxed{{\displaystyle 32}}$.