A number is increased by 25% and then decreased by 20%. If the final result is 9

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Question: A number is increased by 25% and then decreased by 20%. If the final result is 96, what was the original number?

Options:

Correct Answer: 100

Solution:

Let the original number be x. The equation is: x * 1.25 * 0.8 = 96. Simplifying gives x = 96 / 1 = 120, so the original number is 100.

A number is increased by 25% and then decreased by 20%. If the final result is 96, what was the original number?

A number is increased by 25% and then decreased by 20%. If the final result is 96, what was the original number?

Step 1: Let the original number be represented as 'x'.
Step 2: When the number is increased by 25%, it becomes 'x * 1.25'.
Step 3: Next, we decrease this new number by 20%. To do this, we multiply by 0.8: 'x * 1.25 * 0.8'.
Step 4: We know that after these changes, the final result is 96. So we set up the equation: 'x * 1.25 * 0.8 = 96'.
Step 5: Simplify the left side of the equation: '1.25 * 0.8 = 1'. Therefore, the equation becomes 'x = 96 / 1'.
Step 6: Calculate '96 / 1', which equals 96. So, 'x = 120'.
Step 7: The original number is 120.

Percentage Increase and Decrease – Understanding how to apply percentage changes sequentially to a number.
Algebraic Manipulation – Setting up and solving equations based on the problem statement.