In a test, the average marks scored by 20 students of a class is 43 and those by the remaining students is 47.5. If the average marks scored by all the students of the class is 45, then how many students are there in the class?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 36
The total marks of the two groups must equal the total marks of the whole class at its average.
Assuming the number of remaining students to be \(n\):
Total of the 20 students \(=20\times43=860\)
Total of the others \(=47.5n\); total of the class \(=45(20+n)\)
\(860+47.5n=900+45n\)
\(2.5n=40\), so \(n=16\)
Students in the class \(=20+16=\) 36
Shortcut:
The group of 20 is 2 marks below the average (\(45-43\)); the other group is 2.5 marks above it (\(47.5-45\))
The sizes are in the inverse ratio, \(2.5:2=5:4\), so 20 students go with 16
Class \(=20+16=36\)