In a class test, 30 students passed in Mathematics, 30 in Physics, and 35 in Chemistry. 20 students passed in exactly two subjects while 65 passed in at least one of the three subjects. How many passed in all the three subjects?105150
Question
In a class test, 30 students passed in Mathematics, 30 in Physics, and 35 in Chemistry. 20 students passed in exactly two subjects while 65 passed in at least one of the three subjects. How many passed in all the three subjects?105150
Solution
Sure, let's solve this step by step:
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First, let's add up all the students who passed in each subject: 30 (Mathematics) + 30 (Physics) + 35 (Chemistry) = 95 students. This is the total number of passes in all subjects.
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However, we know that 20 students passed in exactly two subjects. This means that these 20 students have been counted twice in our total of 95. To correct this, we need to subtract these 20 students: 95 - 20 = 75 students. Now we have the number of students who passed in either one or three subjects.
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We also know that 65 students passed in at least one of the three subjects. Since we have already accounted for the students who passed in one or two subjects, this number must also include the students who passed in all three subjects.
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Therefore, to find the number of students who passed in all three subjects, we subtract the number of students who passed in one or two subjects (75) from the total number of students who passed in at least one subject (65): 65 - 75 = -10.
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However, a negative number doesn't make sense in this context. This could be due to a mistake in the problem's setup or a misunderstanding of the problem's conditions. Please check the problem again.
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