In an examination 60 candidates offer maths, 80 offer english,and 50 offer physics, if 20 offer maths & english, 15 offer english & physics, 25 offer math & physics and 10 offer all the 3. How many students entered to the examination ?
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To find the total number of students who entered the examination, we need to add the number of students who offered each subject separately. However, we have to ensure that we do not count any student more than once.
Let's calculate the number of students who entered for each subject individually:
1. Math: 60 candidates offered math.
2. English: 80 candidates offered English.
3. Physics: 50 candidates offered physics.
Now, we need to subtract the number of students who offered more than one subject to avoid double counting:
1. Math and English: 20 candidates offered both math and English.
2. English and Physics: 15 candidates offered both English and physics.
3. Math and Physics: 25 candidates offered both math and physics.
Finally, we need to add back the students who offered all three subjects, as they were excluded twice in the above steps:
1. Math, English, and Physics: 10 candidates offered all three subjects.
Let's calculate the total number of students who entered the examination:
Math: 60
English: 80
Physics: 50
Math and English: -20
English and Physics: -15
Math and Physics: -25
Math, English, and Physics: +10
Total = Math + English + Physics - (Math and English) - (English and Physics) - (Math and Physics) + (Math, English, and Physics)
Total = 60 + 80 + 50 - 20 - 15 - 25 + 10
Total = 140
Therefore, a total of 140 students entered the examination.
To find out how many students entered the examination, we need to add up the number of students who offer each subject and then subtract the number of students who offer two subjects and the number of students who offer all three subjects.
Let's break it down step by step:
We are given the following information:
Number of students offering maths = 60
Number of students offering English = 80
Number of students offering Physics = 50
Number of students offering Maths & English = 20
Number of students offering English & Physics = 15
Number of students offering Maths & Physics = 25
Number of students offering all three subjects = 10
To find the number of students who entered the examination, we start by adding up the number of students who offer each subject:
Total number of students offering Maths, English, or Physics = 60 + 80 + 50 = 190
However, this includes the students who offer two subjects and the students who offer all three subjects. To avoid double counting these students, we need to subtract them.
To find the number of students who offer two subjects, we add up the number of students who offer each pair of subjects:
Number of students offering Maths & English = 20
Number of students offering English & Physics = 15
Number of students offering Maths & Physics = 25
Total number of students offering two subjects = 20 + 15 + 25 = 60
Finally, we need to subtract the number of students who offer all three subjects:
Number of students offering all three subjects = 10
Now, we can calculate the number of students who entered the examination:
Number of students who entered the examination = Total number of students offering Maths, English, or Physics - Total number of students offering two subjects - Number of students offering all three subjects
Number of students who entered the examination = 190 - 60 - 10 = 120
Therefore, 120 students entered the examination.