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Question
The mean weight of 150 students in a certain class is 60 kgs. The mean weight of boys in the class is 70 kg and that of girls is 55 kgs. Find the number of boys and the number of girls in the class.
Solution
Let the number of boys and girls in the class be n1 and n2 respectively. Then
n1 + n2 = 150 ...(i)
We have
`bar"X"_1` = Mean weight of boy = 70 kgs.
`bar"X"_2` = Mean weight of girl = 55 kgs.
`bar"X"` = Mean weight of all students = 60 kgs.
∴ `bar"X" = ("n"_1bar"X"_1 + "n"bar"X"_2)/("n"_1 + "n"_2)`
⇒ 60 = `("n"_1 xx 70 + "n"_2 xx 55)/("n"_1 + "n"_2)`
⇒ 60(n1 + n2) = 70n1 + 55n2
⇒ 60n1 + 60n2 = 70n1 + 55n2
⇒ 10n1 = 5n2
⇒ 2n1 = n2 ...(ii)
Putting n2 = 2n1 from (ii) in (i), we get
n1 + 2n1 = 150
⇒ 3n1 = 150
⇒ n1 = 50.
Putting n1 = 50 in n2 = 2n1, we get
n2 = 100.
Hence, there are 50 boys and 100 girls in the class.
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