Question: "The average marks of the students in four sections A,B,C and D together is 60 %. The average marks of the students of A,B,C and D individually are 45%,50%,72% and 80% respectively. If the average marks of the students of sections A and B together is 48% and that of the students of B and C together is 60%.What is the ratio of number of students in sections A and D?"
This particular type of questions conjecture the usage of an applied formulation of known average to estimate the other value. Like four sticks average 600 mm would mean 5th stick to be of length 600 mm only. I am not asking for the theoritical explanation but the details of what the rule actually means.
For example,If the average of two quantity is a particular value then the average of the other two value will be same as the combined average. I think this is a very frequently encountered property but please explain me why this works?