When a certain number is increased by 20, the new value becomes 116% of the original number. What is the original number in this percentage based aptitude question?

Introduction / Context:
This aptitude question is based on basic percentage and linear equations. You are told that when a certain number is increased by 20, the new value becomes 116 percent of the original number. The task is to identify the original number using the relation between percentage change and the corresponding arithmetic expression.

Given Data / Assumptions:
- Let the original number be represented by x.
- When 20 is added to x, the result is 116 percent of x.
- 116 percent means 116/100 times the original number.
- All values are real numbers and there is no rounding involved.

Concept / Approach:
The core idea here is that a statement about percentages can be translated into an algebraic equation. Saying that a new value is 116 percent of the original means new value = 1.16 * original value. We then express the increase of 20 as x + 20 and set it equal to 1.16x. Solving this simple linear equation gives us the original number.

Step-by-Step Solution:
Step 1: Let the original number be x.Step 2: According to the question, x + 20 = 1.16 * x.Step 3: Rearrange the equation to group x terms: x + 20 = 1.16x implies 20 = 1.16x - x.Step 4: Simplify the right side: 1.16x - x = 0.16x, so we have 20 = 0.16x.Step 5: Solve for x by dividing both sides by 0.16, giving x = 20 / 0.16 = 125.Step 6: Therefore, the original number is 125.

Verification / Alternative check:
To verify, start with the found value 125. Increase it by 20 to get 145. Now calculate 116 percent of 125. Since 1 percent of 125 is 1.25, 116 percent is 1.25 * 116 / 100? A more direct method is 1.16 * 125. Compute 1.16 * 125 by 125 * 116 / 100 which equals 145. The new value 145 exactly matches the value obtained by adding 20 to 125, confirming that the solution is correct.

Why Other Options Are Wrong:
Option 80 is too small. If we add 20 we get 100, and 116 percent of 80 is 92, not 100. Option 100 gives 120 when 20 is added, but 1.16 * 100 = 116, so it does not match. Option 150 gives 170 when 20 is added, while 1.16 * 150 = 174, so this also fails. Option 250 gives 270 after adding 20, whereas 1.16 * 250 = 290, which is not equal to 270.

Common Pitfalls:
A common mistake is to interpret 116 percent as simply adding 16 instead of understanding it as 1.16 times the original number. Another error is to write 116x instead of 1.16x, which completely changes the scale of the equation. Some learners also incorrectly set up the equation as x + 20 = x + 1.16, mixing up additive and multiplicative percentage interpretations.

Final Answer:
The original number that becomes 116 percent of itself when increased by 20 is 125.