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Instructions
In a group of 75 students 28 students study Mathematics (M), 32 study Physics (P), 30 study Chemistry (C) and 15 students study none of these; 13 study both M and P, 12 study P and C and 10 study C and M. Based on this information answer the questions.
Solution
Let a = only M
b = only P
c= only C
d = only M and P
e = only M and C
f = only P and C
g = all three
n = none = 15
a+b+c+d+e+f+g+n = 75 => a+b+c+d+e+f+g = 60
X = a+b+c
Y = d+e+f
Z = g
X+2Y + 3Z = 28 + 32 + 30 = 90 ----------------- (1)
d+g = 13
e+g = 10
f+g = 12
Adding we get Y + 3Z = 35 -------------(2)
Subtracting 1 and 2, we get X + Y = 55
=> Z = g = 5
Hence d= 8, e=5 and f = 7 a = 10, b = 12, c= 13
Only physics = b = 12
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