Two numbers are respectively 7% and 28% of a third number. The first number is what percent of the second number?

Introduction / Context:
This question tests the ability to compare two related percentages by using a common base. Many aptitude questions define two numbers as different percentages of a third reference number and then ask for the relative percentage between those two numbers. Understanding how ratios of percentages work is a very useful technique for quickly solving such problems without assigning specific numerical values to the third number.

Given Data / Assumptions:

Let the third number be some reference value, say N.
First number = 7% of N.
Second number = 28% of N.
We need the first number as a percentage of the second number.
All percentages are simple and refer to the same base N.

Concept / Approach:
If two numbers are given as percentages of the same base, we can express them using that base and then take their ratio. Let:
first number = 0.07 * N second number = 0.28 * N To find the first as a percent of the second, we form the fraction (first / second) and then multiply by 100. The base N cancels out, which makes the calculation straightforward.

Step-by-Step Solution:
Step 1: Express both numbers in terms of N. First number = 7% of N = 0.07 * N. Second number = 28% of N = 0.28 * N. Step 2: Compute the fraction of first over second. (first / second) = (0.07 * N) / (0.28 * N). Step 3: Cancel N in numerator and denominator. (0.07 * N) / (0.28 * N) = 0.07 / 0.28. Step 4: Simplify 0.07 / 0.28. 0.07 / 0.28 = 7 / 28 = 1 / 4. Step 5: Convert this fraction into percent. (1 / 4) * 100 = 25%.

Verification / Alternative check:
We can choose a convenient value for N to double-check. Let N = 100 for simplicity. Then the first number is 7% of 100 = 7, and the second number is 28% of 100 = 28. Now find 7 as a percentage of 28: (7 / 28) * 100 = (1 / 4) * 100 = 25%. This matches our earlier result and confirms the correctness of the answer.

Why Other Options Are Wrong:
24% would require the fraction between first and second to be 0.24, but we actually get 0.25.
29% would suggest the first is slightly more than one fourth of the second, which is not supported by the exact 7 and 28 ratio.
34% and 21% are also inconsistent with the exact fraction 1 / 4 obtained from 7 / 28.

Common Pitfalls:
One common mistake is to compare 7 and 28 directly as if they were full numbers without recognising that they both refer to the same base value. Another error is to compute 7% of 28 or 28% of 7 instead of using the correct relationship. Forgetting to multiply the final fraction by 100 to convert it into a percentage is also a frequent source of error. Always remember that percentages of the same base can be compared by taking their simple ratio.

Final Answer:
The first number is 25% of the second number.