In a class, if 50% of the boys were girls, then there would be 50% more girls…
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In a class, if 50% of the boys were girls, then there would be 50% more girls than boys. What percentage of the overall class is girls?
- A.
25%
- B.
33.33%
- C.
40%
- D.
20%
Attempted by 72 students.
Show answer & explanation
Correct answer: D
Solution: find the fraction of the class that are girls.
Let the original number of boys be B and the original number of girls be G.
After converting 50% of the boys into girls, the new number of girls = G + 0.5B, and the new number of boys = 0.5B.
The condition says the new number of girls is 50% more than the new number of boys, so:
G + 0.5B = 1.5 × (0.5B) = 0.75B.
Solve for G: G = 0.75B − 0.5B = 0.25B. Thus G:B = 0.25B:B = 1:4.
Total students = G + B = 0.25B + B = 1.25B, so the fraction of the class that are girls is G/(G+B) = 0.25B / 1.25B = 0.2 = 20%.
Therefore, 20% of the class are girls.
Quick numeric check: take 5 students with 1 girl and 4 boys. Converting half the boys (2) to girls gives 3 girls and 2 boys, and 3 = 1.5 × 2, so the condition holds.