Question

Asin a survey of 25 student it was found that 15 had taken mathematics 12 had taken physics and 11 has taken chemistry 5 had taken mathematics and Chemistry 9 has taken mathematics and physics for had taken Physics and Chemistry and 3 had taken all the three subjects the number of student who had taken only physics is and the

Answer 1

↪M = a +e +c +b = 15
C = f +e + c + d = 11
P = b + c + d + g =12

↪Maths and chemistry = e + c =5
Maths and physics = b + c  = 9
Physics and chemistry = d +c = 4
⭐All three = c = 3 (1)

So using (1) in above three equations, we get
e = 2 , b = 6 ,d = 1
Hence using these three values in the above equation,we get

↪a +e +c +b = 15
Or a = 15 -2-3-6 = 4

f +e + c + d = 11
Or f = 11 - 2-3 -1 = 5

b + c + d + g =12
So g = 12 -6 -3 -1 = 2

So Number of student who have taken atleast one subject = a +  b + c + d +e+ f + g = 4 +6 +3 +1+2+5 +2 = 23
↪And number of student who have taken one subject only = a+f+g = 4 + 5 + 2 = 11

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