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 \( \boxed{32} \).