Percentages on Variables: Find the number of students who took this exam

[Merotzu]

TL;DR Summary: i want to understand the concept.
i denote the students as X,
0.1X students passed all topics
0.1X students did not pass any topics
0.80X remaining students
0.2*0.80X students passed in one topic
0.25*0.80X students passed in 2 topics only
0.24*0.80X students passed in 4 topics only
so going by this pattern
out of the 100 percent of remaining students
(100-20-25-24)*0.80X=500 as 20% of the overall students are students who passed all topics or no topics.But i am not getting the answer

In a practice paper at 2iim.com, questions were given from 5 topics. Out of the appearing students, 10% passed in all topics while 10% did not pass in any. Of the remaining, 20% passed in one topic only and 25% in two topics only. If 24% of the total students passed 4 topics only and 500 students passed in 3 topics only, find the total number of students who appeared in the examination?

 

[berkeman]

Please show us your work on this question. We are not allowed to provide tutorial assistance until you show your work. Thank you.

 

[Merotzu]

below is the attached problem file

 

[Merotzu]

could you take a moment and tell me what is the logical mistake in the solution of my problem

 

[berkeman]

Out of the appearing students, 10% passed in all topics while 10% did not pass in any. Of the remaining, 20% passed in one topic only and 25% in two topics only. If 24% of the total students passed 4 topics only and 500 students passed in 3 topics only, find the total number of students who appeared in the examination?

Sorry if you saw my initial feedback on the problem before I deleted it. The question is pretty confusing the way they are stating it, but here is my attempt to start it (so we can compare my work to yours):

Problems	Pass
--------	------------
5		     10%
4		     24%
3		     500 total
2		     25% * 80%
1		     20% * 80%		
0		     10%

So adding up the percentages will give you the percentage left that equals the 500. What percentage did you get for that group?

 

[Merotzu]

i got 2016 approximately.But the correct answer is 2500

 

[FactChecker]

So adding up the percentages will give you the percentage left that equals the 500. What percentage did you get for that group?

i got 2016 approximately

That's not what he asked. First, you need to know what percent of the total the 500 is.

 

[Merotzu]

i think it is 31 percent of the remaining 80 percent of the students.But i am getting the wrong answer by doing in this method

 

[berkeman]

But the correct answer is 2500

Yes, that is what I get using my table above.

 

[FactChecker]

i think it is 31 percent of the remaining 80 percent of the students.But i am getting the wrong answer by doing in this method

That is wrong. Convert the percentages of the 80% into percentages of the total. Subtracting all the known percentages of the total, what do you get as the remaining percent of the total for the 500 who passed exactly 3 topics?