What is 80% of a number if 200% of the same number equals 90?
Aptitude
Percentage
Difficulty: Easy
Choose an option
Answer
Correct Answer: 36
Explanation
Introduction / Context:This question tests proportional scaling among percentages of the same base number. Knowing one percentage value allows quick determination of another percentage by ratio.Given Data / Assumptions:
- Let the number be N.
- 200% of N = 90.
- We want 80% of N.
Concept / Approach:From 200% of N = 2N = 90, deduce N = 45. Then compute 80% of N = 0.8 * 45. Alternatively, scale directly: 80% is 0.8/2.0 = 40% of the given 200% value → 0.4 * 90 = 36.Step-by-Step Solution:
2N = 90 ⇒ N = 45.80% of N = 0.8 * 45 = 36.Verification / Alternative check:Direct scaling: (80% / 200%) * 90 = (0.8 / 2.0) * 90 = 0.4 * 90 = 36. Matches.
Why Other Options Are Wrong:
- 72 and 144: These correspond to doubling or quadrupling errors; not consistent with N = 45.
- None of these: Not needed because 36 is correct and listed.
Common Pitfalls:Confusing 200% with 20% or dividing 90 by 0.8 instead of by 2 first.
Final Answer:
36