Question

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.

Answer 1

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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