In a Physics test, the average marks of girls in a class is 40. If the average marks of first 20 girls is 50 and that of the remaining girls is 20, then total number of girls in the class is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 30
The total marks of the class equal the total of the two groups, and each total is the average times the number of girls.
Let the class have \(n\) girls; class total \(=40n\)
First 20 girls: \(20\times50=1000\) marks
Remaining \(n-20\) girls: \(20(n-20)\) marks
The two groups make up the class: \(1000+20(n-20)=40n\)
\(600+20n=40n\)
\(20n=600\), so \(n=30\)
Shortcut: The class average 40 lies between the two group averages, and the group sizes are in the inverse ratio of the distances from it.
Distances from 40: \(50-40=10\) and \(40-20=20\)
So the first group : remaining girls \(=20:10=2:1\)
The first group is 20 girls, so the rest are 10 and the class has 30 girls