Thirty six students of class IX contributed on an average ₹42 towards flood relief fund whereas some students of class X contributed on an average ₹54.50. If the overall average contribution per student remained ₹47, then how many students of class X contributed?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 24
The total contribution of both classes equals the overall average times the total number of students. Let \(n\) students of class X contribute.
Class IX: \(36\times42=1512\)
Class X: \(54.50n\)
Both classes together: \(47(36+n)=1692+47n\)
\(1512+54.5n=1692+47n\)
\(7.5n=180\), so \(n=24\)
Shortcut: By alligation, the numbers of students are in the inverse ratio of their distances from the overall average.
Class IX is \(47-42=5\) below the average; class X is \(54.50-47=7.50\) above it
Class IX : class X \(=7.5:5=3:2\)
3 parts are 36 students, so 2 parts are 24 students