Two numbers are respectively 40% and 30% more than a third number. The second number, when expressed as a percentage of the first number, is equal to:

Introduction / Context:
This question tests understanding of percentage increase and comparison between numbers that are related to a common base. The idea is to express two numbers in terms of a third reference number and then compare them as a percentage. Such problems are common in percentage and ratio based aptitude questions and help develop comfort with relative comparisons.

Given Data / Assumptions:

• Let the third number be T.
• The first number is 40% more than T.
• The second number is 30% more than T.
• We need to find the second number as a percentage of the first number.

Concept / Approach:
A standard technique is to assume a convenient value for the base number T, such as T = 100, to simplify the percentage calculations. Then the first and second numbers are expressed in terms of T. Once both numbers are written numerically, we compute the ratio of the second to the first and convert this ratio into a percentage. This is more reliable than trying to directly work with percentage expressions without a numeric base.

Step-by-Step Solution:
Step 1: Assume T = 100 for simplicity. Step 2: First number = T increased by 40% = 100 + 40 = 140. Step 3: Second number = T increased by 30% = 100 + 30 = 130. Step 4: We need second as a percentage of first, that is (Second / First) * 100. Step 5: Compute ratio: 130 / 140. Step 6: 130 / 140 = 13 / 14. Step 7: Multiply by 100 to get percentage: (13 / 14) * 100 ≈ 92.857%. Step 8: Rounded to one decimal place, this is approximately 92.8%.

Verification / Alternative check:
We can cross check by approximating. Since both numbers are close to each other, the second number is slightly less than the first. If the first is 140 and the second is 130, the difference is 10, which is about 7.14% of 140. So the second is roughly 100% minus 7.14%, which is about 92.86%. This matches our earlier calculation of about 92.8%, confirming the result.

Why Other Options Are Wrong:
84.23%, 87.14%, and 94.1% are not consistent with the exact ratio 13 / 14. These values would correspond to different numerical relationships between the first and second numbers. The option 100% would imply both numbers are equal, which is not true because one is 140 and the other is 130. Only 92.8% correctly represents the ratio of the second number to the first based on the given conditions.

Common Pitfalls:
Many learners incorrectly compare 40% and 30% directly and assume a simple difference of 10% as the answer, which is wrong. The percentages are taken with respect to the third number T, not directly between the first and second numbers. The correct method is to convert both to concrete values using the same base and then compute their ratio. Forgetting to multiply by 100 when converting to a percentage is another common error.

Final Answer:
The second number is 92.8% of the first number.