The average weight of all the students of a class is 55 kg. The ratio of the average weight of the boys to that of the girls is 5 : 4. If 40% of the students are boys and the rest are girls, what is the average weight of the boys?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 62.5 kg
The class average is a weighted average: each group’s average counts in proportion to its share of the students. Taking 100 students makes the shares easy to use.
Take 100 students: 40 boys and 60 girls
Let the average weights be \(5k\) kg for boys and \(4k\) kg for girls
Total weight of the class \(=100\times55=5500\) kg
\(40\times5k+60\times4k=200k+240k=440k\)
\(440k=5500\), so \(\displaystyle k=\frac{5500}{440}=12.5\)
Average weight of the boys \(=5k=5\times12.5=62.5\) kg
The average weight of the boys is 62.5 kg (and of the girls \(4\times12.5=50\) kg).