What should be the minimum no of students in a class room given the following conditions?

Question

What should be the minimum no of students in a class room in which 25% student score 75 marks,10% student score 85 marks,15 % student score less than 50 marks, 25% score 60 marks and remaining student score more than 90 marks..

My Approach:

75 MARKS------------------------------->25%

80 MARKS------------------------------->10%

50 MARKS(LESS THAN)-------------->15%

60 MARKS------------------------------->25%

90 MARKS(REMAINING)------------>25%

How to solve this problem after this as I am unable to do after it?

2)What would be the answer if it would be atleast and almost number of students?

Answer 1

If you take the greatest common divisor of your percentages (which is easy to see is 5), then the minimum number of students is $100 / 5 = 20$ (Why?)

Answer 2

The key to this is understanding that you can't have a fraction of a student. So if 25% (one quarter) of students score 75 marks, that means that the number of students must be a multiple of 4.

Because 10% (one tenth) of students score 80 marks, the number of students must be a multiple of 10.

The 15% sounds trickier. Three twentieths of the number of students must be an integer - how do we accommodate that? But in fact it is not a problem at all. We already know that the number of students must be a multiple of 4 and a multiple of 10. The Lowest Common Multiple of 4 and 10 is 20, so the number of students must be a multiple of 20. If so, then three twentieths of that number will be an integer, so there is no further constraint.