What is 80% of a number if 200% of the same number equals 90?

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:

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: