In a class of 40 students, ratio of boys and girls is 3 : 2 and the average marks scored by boys is 42 and that by girls is 46. Then the average marks scored by the whole class is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 43.6
The class average is the total marks of all the students divided by the number of students; each group’s total is its average times its size.
Boys \(\displaystyle =\frac{3}{5}\times40=24\); girls \(=40-24=16\)
Total marks of the boys \(=24\times42=1008\)
Total marks of the girls \(=16\times46=736\)
Class average \(\displaystyle =\frac{1008+736}{40}=\frac{1744}{40}=43.6\)
Shortcut: The class average lies between 42 and 46, nearer the larger group.
Boys are \(\frac{3}{5}\) of the class and girls \(\frac{2}{5}\), so the average is \(42+\frac{2}{5}\times(46-42)=42+1.6=43.6\)