If a number is increased by 20% and the result is 120, what was the original number?

To find the original number when it has been increased by 20% to reach a result of 120, it's essential to understand the relationship between the original number, the percentage increase, and the final result.

Let’s denote the original number as ( x ). When ( x ) is increased by 20%, it becomes ( x + 0.20x ), which simplifies to ( 1.20x ).

According to the problem, this increased amount equals 120:

[

1.20x = 120

]

To find the value of ( x ), you can solve this equation by isolating ( x ). Start by dividing both sides of the equation by 1.20:

[

x = \frac{120}{1.20}

]

Calculating the right side gives:

[

x = 100

]

This means the original number was 100. When increased by 20%, this results in:

[

100 + (20% \text{ of } 100) = 100 + 20 = 120

]

The calculation confirms that increasing 100 by 20% yields the final result of 120. Therefore, the original number,