SOLUTION: In an examination, 75% students passed in science, 65% passed in mathematics and 15% failed in both the subjects. If the total number of students who passed in both the subjects wa

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Question 175135: In an examination, 75% students passed in science, 65% passed in mathematics and 15% failed in both the subjects. If the total number of students who passed in both the subjects was 475, find the total number of students who appeared in the examination
Answer by psbhowmick(878) About Me  (Show Source):
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In the above figure, S%5Bp%5D represents the set of all students who passed in only Science, M%5Bp%5D represents the set of all students who passed in only Mathematics, SM%5Bp%5D represents the set of all students who passed in both Science and Mathematics and SM%5Bf%5D represents the set of all students who failed in both Science and Mathematics.

Let the total no. of students = N.
So we can write S%5Bp%5D+%2B+M%5Bp%5D+%2B+SM%5Bp%5D+%2B+SM%5Bf%5D+=+N+ ______ (1)

It is given that SM%5Bp%5D+=+475.
Again, S%5Bp%5D+%2B+SM%5Bp%5D+=+0.75N i.e. S%5Bp%5D+%2B+475+=+0.75N.
Also, M%5Bp%5D+%2B+SM%5Bp%5D+=+0.65N i.e. M%5Bp%5D+%2B+475+=+0.65N.
Further, SM%5Bf%5D+=+0.15N.

Substituting these into equation (1)
0.75N+-+475+%2B+0.65N+-+475+%2B+475+%2B+0.15N+=+N+
1.55N+-+475+=+N+
1.55N+-+N+=+475+
0.55N+=+475+
N+=+475%2F0.55+
N+=+95
Thus, a total of 95 students appeared for the examination.