Question

How many students passed in all the three subjects?

• A. 185
• B. 175
• C. 170
• D. 171
• E. Cannot be determined

Answer 1

The correct option is D 171

Total number of students =280
Number of students who passed in Maths =185
Number of students who passed in Physics =210
Number of students who passed in Chemistry=222
Number of students who passed in Maths and Physics =180
Number of students who passed in Maths and Chemistry =175
Number of students who passed in Physics and Chemistry =200
Number of students who passed in at least one subject =280-47=233

x+2=180....(i)
w+z=200....(ii)
w+y=175....(iii)
M+x+w+y=185....(iv)
P+x+w+z=210.....(v)
C+y+w+z=222....(vi)
M+P+C+y+x+z+w=233......(vii)
By (iv)+(v)+(vi)-(vii),
x+y+z+2w=384....(viii)
by (i)+(ii)+(iii),
x+y+z+3w=555....(ix)
By (ix)-(viii),
w =171
From equation (i),
x=9
From equation (ii),
z=200-171=29
From equation (iii),
y =175-171=4
M=185-4-9-171=1
P=210-9-171-29=1
C=222 -4 -29 -171 =18
Number of students who have have passed in all three subjects =171