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Question

In a class, each student likes either mathematics or science or both. The number of students who like mathematics and science are 248 and 200, respectively.
One-fourth of the students who like mathematics also like science. Find the total number of students in the class.

A
386
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B
448
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C
324
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D
300
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Solution

The correct option is A 386
Number of students who like mathematics = 248
Number of students who like science = 200

The number of students who like both mathematics and science is one-fourth the number of students who like mathematics.

Thus,
Number of students who like both subjects
=14×248=62

Number of students who only like mathematics = 248 – 62 = 186

Number of students who only like science = 200 – 62 = 138

So, showing the number of students in a Venn diagram, we get:


So, total number of students in the class = 186 + 62 + 138 = 386

Thus, there are 386 students in the class.

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