The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is
This is a weighted average problem that can be solved quickly and easily using the method of Alligation. This method helps find the ratio of two groups when their individual averages and the combined average are known.
We set up a diagram to find the ratio of boys to girls. We find the difference between the combined average and each group's average diagonally.
- The result from the alligation gives us the ratio of the number of boys to the number of girls.
- Ratio of (Number of Boys : Number of Girls) = 8 : 2, which simplifies to 4 : 1.
- This ratio means that for every 4 boys in the class, there is 1 girl.
- The total number of "parts" in the class is 4 (boys) + 1 (girl) = 5.
- The percentage of boys is the fraction of boys' parts out of the total parts:
(4 / 5) × 100% = 80%
Final Answer: The percentage of boys in the class is 80%.
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