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.
All those except 5 students who passed in Maths, passed in Physics.
All those except 10 students who passed in Maths, passed in Chemistry.
47 students failed in all the three subjects.
200 students who passed in Physics also passed in Chemistry.
A student has to pass in at least two subjects to get promoted. How many students get promoted?
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 :
Students who passed in at least 2 subjects = $$w + x + y + z$$
= $$9 + 29 + 4 + 171 = 213$$
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