Out of total 150 students, 45 passed in Accounts, 30 in Economics and 50 inMaths, 30 in both Accounts and Maths, 32 in both Maths and Economics, 35 inboth Accounts and Economics, 25 students passed in all the three subjects. Findthe numbers who passed atleast in anyone of the subjects:(a) 63(b) 53(c) 73(d) None
Question
Out of total 150 students, 45 passed in Accounts, 30 in Economics and 50 inMaths, 30 in both Accounts and Maths, 32 in both Maths and Economics, 35 inboth Accounts and Economics, 25 students passed in all the three subjects. Findthe numbers who passed atleast in anyone of the subjects:(a) 63(b) 53(c) 73(d) None
Solution
To solve this problem, we can use the principle of inclusion and exclusion.
First, we add the number of students who passed in each subject:
45 (Accounts) + 30 (Economics) + 50 (Maths) = 125
Then, we subtract the number of students who passed in two subjects because we have counted them twice:
125 - 30 (Accounts and Maths) - 32 (Maths and Economics) - 35 (Accounts and Economics) = 28
Finally, we add back the number of students who passed in all three subjects because we have subtracted them twice:
28 + 25 (all three subjects) = 53
So, the number of students who passed in at least one of the subjects is 53. Therefore, the correct answer is (b) 53.
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