Scale one percentage to another: If 37 1/2% of a number is 900, then find 62 1/2% of the same number.
Aptitude
Percentage
Difficulty: Easy
Choose an option
Answer
Correct Answer: 1500
Explanation
Introduction / Context:The percentages 37 1/2% and 62 1/2% are complementary to 100% and can be expressed as simple fractions (3/8 and 5/8). This makes computing the whole and rescaling straightforward.
Given Data / Assumptions:
- 37.5% = 3/8 of the number equals 900.
- We seek 62.5% = 5/8 of the number.
Concept / Approach:From (3/8) * N = 900, solve for N. Then compute (5/8) * N for the desired percentage.
Step-by-Step Solution:
(3/8) * N = 900 ⇒ N = 900 * 8 / 3 = 2400.Now compute (5/8) * N = (5/8) * 2400 = 1500.Verification / Alternative check:Check: 3/8 of 2400 is 900 (given) and 5/8 of 2400 is 1500. The two add to the whole 2400, confirming consistency.
Why Other Options Are Wrong:
- 1200 and 1350 are undershoots of 5/8 of 2400.
- 540 corresponds to 22.5% of 2400, not 62.5%.
- 1800 equals 75% of 2400, not 62.5%.
Common Pitfalls:Not recognizing the handy fraction forms of 37 1/2% and 62 1/2%, which greatly simplify the arithmetic.
Final Answer:1500