Instructions

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.

Question 107

# How many students passed in all the three subjects ?

Solution

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)

=> $$x + y + z + 3w = 555$$ ------------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 all the three subjects = $$w = 171$$