When a certain number is increased by 24, it becomes 110% of its original value.\nWhat is the original number?

Introduction / Context:
This question checks your understanding of percentage increase and how to convert a statement about increased value into an equation involving the original number. It is a typical reverse percentage problem that can be solved quickly using simple algebra, which is useful in many aptitude tests.

Given Data / Assumptions:

• The original number increases by 24 units.
• After increasing by 24, the new value is 110% of the original number.
• We need to find the original number before the increase.

Concept / Approach:
If the original number is N, then a 10% increase corresponds to multiplying N by 1.10. The statement "becomes 110% of itself" means that the final value is 1.10 * N. Since the final value is also equal to N + 24, we can equate N + 24 with 1.10 * N and solve for N. This is a straightforward linear equation in one variable.

Step-by-Step Solution:
Step 1: Let the original number be N.Step 2: The new value after increase is N + 24.Step 3: The question says this new value is 110% of the original, so N + 24 = 1.10 * N.Step 4: Rewrite the equation as N + 24 = 1.10 N.Step 5: Subtract N from both sides to get 24 = 0.10 N.Step 6: Solve for N: N = 24 / 0.10 = 240.

Verification / Alternative check:
Check the result by direct substitution. If the original number is 240, a 10% increase is 240 * 10 / 100 = 24, so the new number becomes 240 + 24 = 264. Now compute 110% of 240: 240 * 110 / 100 = 240 * 1.10 = 264. Since both calculations lead to 264, the result N = 240 is verified.

Why Other Options Are Wrong:
If N = 288, then 110% of 288 would be 316.8, which is not 288 + 24.
If N = 360, 110% of 360 is 396, while 360 + 24 = 384.
If N = 216, 110% of 216 is 237.6, not 240.
The smaller value 120 gives 110% = 132, whereas 120 + 24 = 144, again not equal.

Common Pitfalls:
Common errors include interpreting 110% as 10% or adding 24 as if it were 10% of the new value instead of the original. Another mistake is to treat 24 as 10% of the final value instead of the original, which leads to a wrong equation. To avoid confusion, always define the original number as a variable, translate the language about percentages into a clear algebraic equation, and then solve systematically.

Final Answer:
The original number is 240.