30% of a number exceeds 25% of the same number by 27. What is the value of the number?

Introduction / Context:
This question tests basic percentage and algebra skills. You are told that 30 percent of a number is greater than 25 percent of the same number by 27. From this information, you must determine the original number. Such problems are very common in quantitative aptitude exams and involve translating verbal statements into algebraic equations using percentage notation.

Given Data / Assumptions:

- Let the unknown number be N. - 30% of N is written as 30/100 * N. - 25% of N is written as 25/100 * N. - The difference between these two quantities is 27.

Concept / Approach:
The key idea is to express the given percentage statements in algebraic form and then solve a simple linear equation. Since both percentages refer to the same number N, their difference is just a fixed percentage of N. Once we compute that percentage, we can equate it to 27 and solve for N by basic division. Working systematically minimizes errors and makes the computation straightforward.

Step-by-Step Solution:
Step 1: Let the number be N. Step 2: Write 30% of N as (30 / 100) * N = 0.30N. Step 3: Write 25% of N as (25 / 100) * N = 0.25N. Step 4: According to the question, 30% of N exceeds 25% of N by 27. That is, 0.30N - 0.25N = 27. Step 5: Simplify the left side: 0.30N - 0.25N = 0.05N. Step 6: So we have 0.05N = 27. Step 7: Solve for N by dividing both sides by 0.05: N = 27 / 0.05. Step 8: Note that 0.05 = 5 / 100 = 1 / 20, so dividing by 0.05 is the same as multiplying by 20. Step 9: Compute N = 27 * 20 = 540.

Verification / Alternative check:
Check the answer by substituting N = 540 back into the original statements. Compute 30% of 540: (30 / 100) * 540 = 0.30 * 540 = 162. Compute 25% of 540: (25 / 100) * 540 = 0.25 * 540 = 135. The difference 162 - 135 is 27, which matches the condition in the question. This confirms that N = 540 is correct.

Why Other Options Are Wrong:
If N = 270, then 30% is 81 and 25% is 67.5, giving a difference of 13.5, not 27. For N = 108, 30% is 32.4 and 25% is 27, giving difference 5.4. For N = 90, 30% is 27 and 25% is 22.5, difference 4.5. None of these differences equal 27, so these options are incorrect.

Common Pitfalls:
Some learners mistakenly add the percentages instead of subtracting them or miscalculate the percentage values. Others might assume that the difference 5% directly equals 27, forgetting that it is 5% of N, not 5% of 100. Carefully translating the verbal description into the equation 0.05N = 27 prevents these errors.

Final Answer:
The value of the number is 540, which corresponds to option A.