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Study the following information carefully to answer these questions : For an examination consisting of three subjects-Maths, Physics and Chemistry, 280 students appeared. When the results were declared, 185 students had passed in Maths, 210 had passed in Physics and 222 had passed in Chemistry.
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By: anil on 05 May 2019 01.39 am
Number of students = 280 Students who passed in Maths = $$m + x + w + y = 185$$ ----------Eqn(1) Students who passed in Physics = $$p + x + w + z = 210$$ --------Eqn(2) Students who passed in Chemistry = $$c + y + w + z = 222$$ ------------Eqn(3) Now, Students who passed in Maths and Physics = $$x + w = 185 - 5 = 180$$ ------------Eqn(4) Students who passed in Maths and Chemistry = $$w + y = 185 - 10 = 175$$ ------------Eqn(5) Students who passed in Physics and Chemistry = $$z + w = 200$$ ------------Eqn(6) Number of Students who passed in at least one subject = $$m + p + c + w + x + y + z = 280 - 47 = 233$$ ------------Eqn(7) Now, adding equations (1),(2) and (3) and subtracting eqn(7) from it, we get : => $$x + y + z + 2w = 384$$ ------------Eqn(8) Adding Eqn (4),(5) and (6) => $$x + y + z + 3w = 555$$ ------------Eqn(9) Now, equation (9)-(8) => $$w = 171$$ Putting it in equation (4), we get $$x = 9$$ Similarly, solving all equations , the required value of the variables are : Number of students who passed in chemistry only = $$c = 18$$
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