Linked percentages across variables: If 90% of A equals 30% of B and B = C% of A, find the value of C.
Aptitude
Percentage
Difficulty: Easy
Choose an option
Answer
Correct Answer: 300
Explanation
Introduction / Context:This item connects two percentage relationships among A, B, and C. The goal is to express B as a percent of A once we compare 90% of A with 30% of B.
Given Data / Assumptions:
- 0.90A = 0.30B.
- B = (C/100) * A.
Concept / Approach:Solve the first equation for B in terms of A, then equate it to (C/100) * A. Cancel A (assuming A ≠ 0), and solve for C.
Step-by-Step Solution:
From 0.90A = 0.30B ⇒ B = (0.90/0.30)A = 3A.But B is also (C/100)A.So (C/100)A = 3A ⇒ C/100 = 3 ⇒ C = 300.Verification / Alternative check:Check: If B = 300% of A, then 30% of B = 30% of 3A = 0.90A, which matches the left side.
Why Other Options Are Wrong:
- 900, 800, 600 are multiples that do not satisfy both relationships simultaneously.
- 150 would make B = 1.5A; then 30% of B would be 0.45A, not 0.90A.
Common Pitfalls:Solving 0.90/0.30 incorrectly or forgetting that “B = C% of A” means (C/100) * A.
Final Answer:300