80 boys took the examination in the three subjects: Chinese, English and Mathematics, and none of them failed in all three subjects. It was noted that 8 passed in English only and 10 passed in Mathematics only; 7 passed in Mathematics and Chinese but not in English, 40 passed in English and Mathematics and 21 passed in English and Chinese, Altogether, 54 passed in English.
Find:
1)How many pupils passed in Chinese only,
2) How many pupils passed in all three subjects.
Here there are total 54 students who passed in English,while there are total 21 students who passed in both E and C.let say if there are x students common in all passed then
54= (21-x)+x+(40-x)+8
x=15
So in all three subjects there are 15 students who passed.
now
80=54+57+(6+15+7+x)-21-40-22+15
HERE x denotes students passed in chinese only
x=9
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To find the number of pupils who passed in Chinese only, we need to analyze the information given.
Let's break down the information:
- 8 students passed in English only.
- 10 students passed in Mathematics only.
- 7 students passed in Mathematics and Chinese but not in English.
- 40 students passed in English and Mathematics.
- 21 students passed in English and Chinese.
- 54 students passed in English (the total number of students who passed in English).
To find the number of students who passed in Chinese only, we need to subtract the number of students who passed in English and Chinese from the total number of students who passed in Chinese. Therefore, Chinese only = Chinese - (Chinese and English).
Chinese only = (English and Chinese) - (English and Mathematics and Chinese).
Now, let's calculate each value:
Step 1: Find (English and Chinese) = 21 students.
Step 2: Find (English and Mathematics and Chinese) = (English and Mathematics) - (English and Chinese).
(English and Mathematics) = 40 students.
(English and Mathematics and Chinese) = 7 students, as given.
Therefore, (English and Chinese) = (English and Mathematics) - (English and Mathematics and Chinese) = 40 - 7 = 33 students.
Step 3: Find Chinese only = (English and Chinese) - (English and Mathematics and Chinese) = 33 - 7 = 26 students.
1) The number of pupils who passed in Chinese only is 26.
To find the number of pupils who passed in all three subjects, we need to subtract the number of students who passed in English only, Mathematics only, and Chinese only from the total number of students who passed in English, Mathematics, or Chinese.
Step 1: Find (English only) = 8 students.
Step 2: Find (Mathematics only) = 10 students.
Step 3: Find (Chinese only) = 26 students.
Step 4: Total students who passed in English, Mathematics, or Chinese = 54 students.
Therefore, number of pupils who passed in all three subjects = Total students who passed in English, Mathematics, or Chinese - (English only + Mathematics only + Chinese only).
Number of pupils who passed in all three subjects = 54 - (8 + 10 + 26) = 54 - 44 = 10 students.
2) The number of pupils who passed in all three subjects is 10.
To solve this problem step-by-step, we can start by adding up the number of students who passed in the different subject combinations:
- Passed in English only: 8
- Passed in Mathematics only: 10
- Passed in Mathematics and Chinese but not in English: 7
- Passed in English and Mathematics: 40
- Passed in English and Chinese: 21
Now, let's find the total number of students who passed in English. We know this to be 54.
1) How many pupils passed in Chinese only:
To find the number of pupils who passed in Chinese only, we need to subtract the number of students who passed in English and Chinese from the total number of students who passed in Chinese.
- Total number of students who passed in Chinese: Passed in Mathematics and Chinese but not in English + Passed in English and Chinese = 7 + 21 = 28
- Number of pupils who passed in Chinese only: Total number of students who passed in Chinese - Passed in English and Chinese = 28 - 21 = 7
Therefore, 7 pupils passed in Chinese only.
2) How many pupils passed in all three subjects:
To find the number of pupils who passed in all three subjects, we need to subtract the number of students who passed in only English, only Mathematics, and only Chinese from the total number of students who passed in English, Mathematics, or Chinese.
- Total number of students who passed in English, Mathematics, or Chinese: Passed in English + Passed in Mathematics + Passed in Chinese = 54
- Number of pupils who passed in all three subjects: Total number of students who passed in English, Mathematics, or Chinese - Passed in English only - Passed in Mathematics only - Passed in Chinese only = 54 - 8 - 10 - 7 = 29
Therefore, 29 pupils passed in all three subjects.