# Can you find out the total number of students?

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In a school, 280 students studied chemistry, 254 students studied physics and 280 students studied biology.

97 students studied chemistry as well as physics, 138 students studied physics as well as biology and 152 students studied chemistry as well as biology.

73 students studied all the three branches.

Can you find out the total number of students?

posted Jul 31, 2015

+1 vote

500 students
.
73 students study all three subjects
97 study chemistry and physics, but we have already counted 73 of them, leaving an additional 24 students
65 students study only physics and biology (138-73)
79 students study only chemistry and biology (152-73)

At this point 176 students study chemistry, meaning 104 students study only chemistry (280-176)
162 already study physics, meaning 92 students study only physics (254-162)
217 already study biology, leaving 63 students who study only biology (280-63)

Total students is then 73 + 24 + 65 + 79 + 104 + 92 + 63 = 500

(quote)"At this point 176 students study chemistry, meaning 104 students study only chemistry (280-104)"(unquote)
You make a mistake here. It should be:
"At this point 103 students (24+79) study chemistry, meaning 177 students study only chemistry (280-103)"
etc....
Total students is then: 73 + 24 + 65 + 79 + 177 + 92 + 63 = 573
Note: It is much easier if we use Venn Diagram to solve this problem.
97 students chemistry + physics and 79 students study chemistry + biology.
97 + 79 = 176 students already studying chemistry.
But there is an error. The final calculation should be:
73 + 24 + 65 + 79 + 104 + 92 + 63 = 500 students.

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