In a percentage aptitude question, the difference between two numbers is equal to 20% of the larger number. If the smaller number is 20, what is the value of the larger number?

Introduction / Context:
This question tests a very common percentage relationship between two numbers, where the difference is expressed as a percentage of the larger number. Such questions are frequently asked in aptitude and bank exams because they check whether a learner can convert a verbal condition into a simple algebraic equation and then solve it correctly. Understanding this type of problem also helps in solving questions related to profit, loss, and discounts where similar percentage relationships appear.

Given Data / Assumptions:

• There are two numbers: one is larger and the other is smaller.
• The difference between the larger and smaller number is equal to 20% of the larger number.
• The smaller number is given as 20.
• We assume both numbers are real and positive, as is usual in basic aptitude problems.

Concept / Approach:
The key idea is to represent the larger and smaller numbers using algebraic symbols and then use the percentage relationship. Percentages can be written as fractions or decimals. Here, 20% of the larger number is written as (20/100) * larger or 0.2 * larger. The difference between the two numbers is then equated to this expression, and we solve the resulting linear equation in one variable. This straightforward algebraic approach is the most systematic method and avoids trial and error.

Step-by-Step Solution:
Step 1: Let the larger number be L and the smaller number be S = 20.Step 2: The difference between the larger and smaller number is L - S.Step 3: According to the question, L - S is equal to 20% of the larger number, so L - S = (20/100) * L.Step 4: Substitute S = 20 to get L - 20 = (20/100) * L.Step 5: Simplify the right side to get L - 20 = 0.2 * L.Step 6: Bring terms in L to one side: L - 0.2 * L = 20.Step 7: This gives 0.8 * L = 20.Step 8: Divide both sides by 0.8 to get L = 20 / 0.8 = 25.

Verification / Alternative check:
To verify, take the larger number as 25 and the smaller number as 20. The difference is 25 - 20 = 5. Now compute 20% of the larger number: 20% of 25 = (20/100) * 25 = 5. Since the calculated difference (5) matches 20% of the larger number (5), the obtained value L = 25 is fully consistent with the given condition. This confirms that the answer is correct.

Why Other Options Are Wrong:
Option 15 is too small because the larger number must be greater than 20, not less than the smaller number. Option 35 gives a difference of 35 - 20 = 15, while 20% of 35 is 7, which does not match. Option 45 gives a difference of 25, but 20% of 45 is 9, so it fails the condition. Option 30 gives a difference of 10, but 20% of 30 is 6, again not equal to the required difference. Hence these options do not satisfy the percentage relationship stated in the problem.

Common Pitfalls:
A very common mistake is to take 20% of the smaller number instead of the larger number. Another error is to subtract 20 directly from the larger number assuming that 20% means subtracting 20 units, which is incorrect because 20% is a relative measure, not an absolute number. Some learners also wrongly assume that the larger number is 20 more than the smaller number without applying the percentage relationship. Careful reading and setting up the correct equation is essential to avoid these mistakes.

Final Answer:
The larger number is 25.