The number of students who study only Chemistry is

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 chemistry = c = 13