Boys to girls ratio from a percent relation: In a school, 10% of the boys equals one-fourth of the girls. What is the ratio of boys to girls?
Aptitude
Percentage
Difficulty: Easy
Choose an option
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A3 : 2
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B5 : 2
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C2 : 1
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D4 : 3
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E5 : 3
Answer
Correct Answer: 5 : 2
Explanation
Introduction / Context:We translate a sentence connecting percentages of groups into an algebraic relation to obtain a ratio.
Given Data / Assumptions:
- B = number of boys; G = number of girls.
- 10% of boys = one-fourth of girls ⇒ 0.10B = 0.25G.
Concept / Approach:Rearrange to B/G by isolating terms.
Step-by-Step Solution:
0.10B = 0.25G.B/G = 0.25 / 0.10 = 2.5.Express as a ratio: 2.5 : 1 = 5 : 2.Verification / Alternative check:Pick numbers matching 5 : 2, e.g., B = 50, G = 20. Then 10% of boys = 5; one-fourth of girls = 5. Condition satisfied.
Why Other Options Are Wrong:
- 3 : 2, 2 : 1, 4 : 3, 5 : 3 do not satisfy 0.10B = 0.25G.
Common Pitfalls:Inverting the ratio (2 : 5) or mixing percent with fraction improperly.
Final Answer:5 : 2