In a class of 40 students 18 passed economics 19 passed accounts 16 passed economics 6 passed mathematics only 9 passed accounts only 5 passed mathematics and accounts only 2 passed accounts and economics only. How many failed in all the papers? How many failed in economics? How many failed in accounts?
Assuming you meant 16 passed math,
Draw your Venn diagram and start filling in the missing pieces.
3 passed all three subjects
7 passed E and M
1 passed M only
So, 33 passed something.
I expect you can take it from there.
To find the number of students who failed in all papers, we need to add up the number of students who passed each subject individually and subtract it from the total number of students in the class.
Step 1: Calculate the number of students who passed each subject individually.
- Passed Economics: 18 + 16 + 2 + 5 (Passed economics only + Passed economics and accounts only) = 41
- Passed Accounts: 19 + 2 + 9 (Passed accounts only + Passed accounts and economics only) = 30
- Passed Mathematics: 6 + 5 (Passed mathematics only + Passed mathematics and accounts only) = 11
Step 2: Calculate the number of students who failed each subject.
- Failed Economics: Total number of students - Number of students who passed economics = 40 - 41 = -1 (Since it cannot be negative, we consider it zero)
- Failed Accounts: Total number of students - Number of students who passed accounts = 40 - 30 = 10
- Failed Mathematics: Total number of students - Number of students who passed mathematics = 40 - 11 = 29
So, in summary:
- Number of students who failed in all papers = 0
- Number of students who failed in economics = 0
- Number of students who failed in accounts = 10
To find the number of students who failed in all the papers, we need to find the total number of students and subtract the number of students who passed in at least one paper.
1. First, find the number of students who passed in at least one paper:
- Number of students who passed economics = 18
- Number of students who passed accounts = 19
We can add these two numbers together to get the total number of students who passed in at least one paper:
18 + 19 = 37
2. Next, find the total number of students in the class:
- Number of students in the class = 40
3. Now, subtract the number of students who passed in at least one paper from the total number of students:
40 - 37 = 3
Therefore, 3 students failed in all the papers.
To find the number of students who failed in economics, we need to subtract the number of students who passed economics from the total number of students.
1. First, find the total number of students who passed economics, taking into account the overlapping students who passed accounts only and passed accounts and economics only:
- Number of students who passed economics = 18
- Number of students who passed accounts only = 9
- Number of students who passed accounts and economics only = 2
To get the total number of students who passed economics, we can add these three numbers together:
18 + 9 + 2 = 29
2. Next, subtract the number of students who passed economics from the total number of students:
40 - 29 = 11
Therefore, 11 students failed in economics.
To find the number of students who failed in accounts, we follow the same steps as finding the number of students who failed in economics.
1. First, find the total number of students who passed accounts, taking into account the overlapping students who passed economics only and passed accounts and economics only:
- Number of students who passed accounts = 19
- Number of students who passed economics only = 2
- Number of students who passed accounts and economics only = 2
To get the total number of students who passed accounts, we can add these three numbers together:
19 + 2 + 2 = 23
2. Next, subtract the number of students who passed accounts from the total number of students:
40 - 23 = 17
Therefore, 17 students failed in accounts.