Question

In a test called ACSAT, the average marks of $15$ test takers are $240$. If the marks of $5$ test takers are subtracted, the average marks decreased by $40$. What are the average marks of $5$ test takers?

Answer 1

Hint: To do this particular question one should know how to find the average of marks or any other quantity. One should also know how to deal with the problems in which some kind of inclusion or exclusion is going on because there we have to find the new total of quantity mentioned in the question.

Complete step-by-step solution:
In the given question, we have
The average mark is $240$.
 The total number of test takers is $15$ .
Therefore, the total marks of all $15$ test takers are $240 \times 15\, = \,3600$.
As it is given in the question that the marks of $5$ test takers are subtracted and the average marks of remaining $10$ students are decreased by $40$.
So,
The total marks of the $10$ test-takers, excluding the $5$ test-takers are,
$ \Rightarrow 240 - 40 = 200$
Total $ \Rightarrow 200 \times 10 = 2000$
Now, the total of the five excluded test-takers is $3600 - 2000\, = \,1600$.
Now, the average marks of five test-takers are $\dfrac{{1600}}{5} = 320$ marks.
Therefore, the average marks of $5$ test-takers are $320$ marks.

Note: There can be several variations in these types of questions. Apart from subtraction there can also be addition or multiplication in the quantities whose effect we can see on average. There are some other quantities which also affect due to these changes like variance and standard deviation.