When an unknown number is increased by 24, the new value becomes 104% of that same original number.\nBased on this percentage relationship, what is the value of the original number before the increase?

Introduction / Context:
In this aptitude question we work with a simple percentage relationship between an unknown number and its increased value. The number is increased by a fixed amount and the result is expressed as a percentage of the original number. Such problems test comfort with converting a verbal percentage statement into an algebraic equation and then solving for the unknown. Understanding this type of question is important for many exam topics like profit and loss, interest, and data interpretation where similar percentage relationships appear.

Given Data / Assumptions:

• An unknown original number is increased by 24.
• The new value after adding 24 is equal to 104% of the original number.
• We assume all values are real numbers and percentages are applied in the usual arithmetic sense.
• We need to find the original number before the increase.

Concept / Approach:
The key concept is that “104% of the original number” means 104 over 100 times the original number. If we call the original number x, then 104% of x is written as 1.04 * x. The statement in the question directly converts to the equation x + 24 = 1.04 * x. Once this equation is formed, solving it is a simple matter of isolating x on one side by subtracting x from both sides and then dividing by the remaining coefficient. This is a straightforward linear equation in one variable.

Step-by-Step Solution:
Step 1: Let the original number be x. Step 2: After increasing the number by 24, the new value becomes x + 24. Step 3: According to the question, this new value equals 104% of the original number, that is 1.04 * x. Step 4: Set up the equation x + 24 = 1.04 * x. Step 5: Subtract x from both sides to get 24 = 1.04 * x - x. Step 6: Simplify the right side: 1.04 * x - x = 0.04 * x. Step 7: So we have 24 = 0.04 * x. Step 8: Solve for x by dividing both sides by 0.04, giving x = 24 / 0.04. Step 9: Compute 24 / 0.04 = 600, so the original number is 600.

Verification / Alternative check:
We can verify the answer by substituting x = 600 back into the original statement. Increase 600 by 24 to get 624. Next, find 104% of 600. Calculate 1% of 600 as 6, and then 104% is 104 * 6 = 624. The new value 624 matches exactly, so the algebraic solution is correct. This confirms that the original number must be 600 and there is no contradiction in the given data or the derived result.

Why Other Options Are Wrong:
If the original number were 300, then adding 24 gives 324, while 104% of 300 is 312, so option 300 is inconsistent. If the original number were 100, then the new value would be 124, but 104% of 100 is only 104. If the original number were 1200, adding 24 gives 1224, but 104% of 1200 equals 1248. None of these match the required relationship, so these options are incorrect.

Common Pitfalls:
A frequent mistake in such questions is to treat 104% as 1.4 instead of 1.04, which would completely change the equation. Another common error is to add 24 to the percentage value rather than to the original number. Some learners also forget to convert percentages into decimal form before using them in equations. Careful reading of the sentence and stepwise algebraic translation help avoid these issues and lead to the correct answer.

Final Answer:
The original number, before it was increased by 24, is 600.