The mean weight of 150 students in a certain class is 60 kg. The mean weight of boys is 70 kg and that of girls in the class is 55 kg. Find the number of boys and girls in the class.

Options

A. 100 and 50
B. 50 and 100
C. 150 and 100
D. 100 and 150

Answer

A

Explanation

Let the number of boys and girls in the class be `n_(1) and n_(2)` respectively. Then,
`n_(1) and n_(2)=150 " " `…(i)
`bar(X_(1))=` Mean weight of boys = 70 kg
`bar(X_(2))=` Mean weight of girls = 55 kg
`bar(X)=` Mean weight of all students = 60 kg.
`therefore bar(X)=(n_(1)bar(X_(1))+n_(2)bar(X_(2)))/(n_(1)+n_(2))`
`rArr 60=(n_(1)xx70+n_(2) xx55)/(n_(1)+n_(2))`
`rArr 60 (n_(1)+n_(2))=70n_(1)+55n_(2)`
`rArr 60n_(1)+60n_(2)=70n_(1)+55n_(2)`
`rArr 10n_(1)=5n_(2) rArr 2n_(1)=n_(2) `...(ii)
From (i) and (ii), we have `n_(1)=100, n_(2)=50`.
Hence, there are 50 boys and 100 girls in the class.