Question

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 \( \frac{24}{0.75} \):
\[
x = 24 \div 0.75 = 32
\]

So, the original number is \( \boxed{32} \).