There are $3$ classes having $20,25$ and $30$ students respectively having average marks in an examination as $20,25$ and $30$ respectively. If three classes are represented by $A,B$ and $C$ and following is known about the three classes :-
$A \Rightarrow \text{Highest Score} = 22, \text{Lowest Score} =18$
$B \Rightarrow \text{Highest Score} = 31, \text{Lowest Score} =23$
$C \Rightarrow \text{Highest Score = 33}, \text{Lowest Score} =26$
The following operation is performed :-
If $5$ people are transferred from $C$ to $B$, further, $5$ more people are transferred from $B$ to $A$, then $5$ are transferred from $A$ to $B$ and finally, $5$ more are transferred from $B$ to $C$.
What will be the minimum possible average of class $B$ after this set of operation is ?
My solution approach :-
Total marks of $B = 625$
To reduce the sum to the lowest what I thought is that $C$ should give minimum marks student to $B$ and then $B$ should give maximum marks student to $A$ and then $A$ should give minimum marks student to $B$ and then $B$ should give maximum marks student to $C$ back. In equation format it would be ;
Total marks of $B = 625 +(26 \times 5) -(31 \times 5) +(18 \times 5)-(31 \times 5)$
But this isn't working and the correct answer is different. What I am doing wrong? Please help !!!
Thanks in advance !!!
The error in your calculation is that it is not possible to have $10$ people starting in class B with $31$ marks, as that would leave the average of the rest below $23$.
If you take this into account, you may find it is is worth sending some of the students $C \to B \to A$