In a class of 10 students, the average marks
scored by top 9 rankers is 40, whereas the
average score of bottom 9 rankers is 38. What
is the difference between the marks scored by
the first and the last ranker?
Ο Ο Ο
18
O 22
Answers
Answer:
This is the answer to your question.
Explanation:
While all of the other answers (at the time of writing this) did solve this question correctly, none showed how to solve it, so I feel obligated to show how I would solve this problem.
First, I look for what information is important and what is not. At first glance, the information that these values are the average marks out of 10 students seems vital, but in the context of the problem, there is no purpose in knowing this. When it boils down to it, we need to know that out of 50 marks there is an average of 40 marks, and that we need to find the average number of marks out of 25 marks.
Now that we know what information to use, we need to figure out how to use it. After further inspection of the problem, 40 marks out of 50 is truly the fraction 40/50, or in its simplified form, 4/5. Using this knowledge, we can deduce that our solution will also have to do with a fraction, which is out of 25 marks. We can write this as m/25, with m representing the average number of marks out of 25 marks total.
Going one step further, because we know that we are talking about the same thing in the same context (average student marks), we can write these two fractions as equal to each other. Our equation looks like this:
4/5 = m/25
At this point, we can solve this equation with basic algebra. Using the multiplication property of equality (This states that if any equivalent values are multiplied by the same factor, the products will also be equivalent.), we can multiply both sides of our equation by 25. This results in 4/5 becoming 100/5, or simplified as a whole number, 20, and m/25, becoming the isolated variable m. This gives us our final equation:
20 = m
Looking back at the problem, we see that it asks for the average marks of the students out of 25 marks. If we can look back at a previous paragraph in my answer, we can see that m’s value is defined as the average number of marks our of 25 marks total. Using this information, it becomes apparent that m’s value is our solution, and therefore our solution is 20.
Answer:
18
Explanation:
Let the marks scored by the highest scorer be A and that that scored by the lowest scorer be B.
We have to find out what A-B is.
So the total marks of the class can be represented in two ways.
Total Marks = Sum of the highest 9 scorers + lowest scorer = 9*40 + B
Also, total marks = Sum of the lowest 9 scorers + Highest scorer = 9* 38 + A
Equating these two equations,
9*40 + B = 9*38 + A
A - B = (9*40) - (9*38) = 18