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The average marks of the girls in a class is equal to the number of boys and the average marks of boys is equal to the number of girls. If the class average is 4 less than the average of both the boys’ and the girls’ average marks, what will be the number of students in the class?
- a)24
- b)48
- c)50
- d)64
Correct answer is option 'C'. Can you explain this answer?
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And girls, what is the ratio of boys to girls in the class?
Let's assume there are B boys and G girls in the class.
We know that:
- The average marks of the girls is equal to the number of boys, so we can write: G/B = B. This means that the number of girls is equal to the square of the number of boys.
- The average marks of the boys is equal to the number of girls, so we can write: B/G = G. This means that the number of boys is equal to the square of the number of girls.
We also know that the class average is 4 less than the average of both the boys and girls. We can write this as:
(BG)/(B+G) - 4 = (B+G)/2
Simplifying this equation, we get:
2BG - 2(B+G)^2 - 8(B+G) = 0
Substituting G=B^2 (from the first equation), we get:
2B^3 - 2(B^2+B^3)^2 - 8(B^2+B^3) = 0
Simplifying and factoring out 2B, we get:
B(1-2B-2B^2-4) = 0
Ignoring the trivial solution B=0, we get:
1-2B-2B^2-4 = 0
Solving for B using the quadratic formula, we get:
B = (2 ± √20)/4 = (1 ± √5)/2
Since B is the number of boys and G=B^2 is the number of girls, the ratio of boys to girls is:
B/G = B/(B^2) = 1/B = 2/(1 ± √5)
Therefore, the ratio of boys to girls in the class is either 2/(1+√5) or 2/(1-√5).
Let's assume there are B boys and G girls in the class.
We know that:
- The average marks of the girls is equal to the number of boys, so we can write: G/B = B. This means that the number of girls is equal to the square of the number of boys.
- The average marks of the boys is equal to the number of girls, so we can write: B/G = G. This means that the number of boys is equal to the square of the number of girls.
We also know that the class average is 4 less than the average of both the boys and girls. We can write this as:
(BG)/(B+G) - 4 = (B+G)/2
Simplifying this equation, we get:
2BG - 2(B+G)^2 - 8(B+G) = 0
Substituting G=B^2 (from the first equation), we get:
2B^3 - 2(B^2+B^3)^2 - 8(B^2+B^3) = 0
Simplifying and factoring out 2B, we get:
B(1-2B-2B^2-4) = 0
Ignoring the trivial solution B=0, we get:
1-2B-2B^2-4 = 0
Solving for B using the quadratic formula, we get:
B = (2 ± √20)/4 = (1 ± √5)/2
Since B is the number of boys and G=B^2 is the number of girls, the ratio of boys to girls is:
B/G = B/(B^2) = 1/B = 2/(1 ± √5)
Therefore, the ratio of boys to girls in the class is either 2/(1+√5) or 2/(1-√5).
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The average marks of the girls in a class is equal to the number of boys and the average marks of boys is equal to the number of girls. If the class average is 4 less than the average of both the boys’ and the girls’ average marks, what will be the number of students in the class?a)24b)48c)50d)64Correct answer is option 'C'. Can you explain this answer?
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