Solution:
Let, the set of people who like curd be C and the set of people who like milk be M. Then,
n(U) = 100%
n(C) = 70%
n(M) = 60%
n(\(\overline{C\cup M}\)) = 20%
and n(C ∩ M) = 550
To find,
- n(U) = ?
- no(C) = ?
Again let, n(C ∩ M) = x%
Representing above information in venn-diagram we get,
From above venn-diagram,
no(C) + no(M) + n(C ∩ M) + n(\(\overline{C\cup M}\)) = n(U)
Or, (70% -x%) + (60% - x%) + x% + 20% = 100%
Or, 150% - x% = 100%
Or, x% = 50%
∴ n(C ∩ M) = 50%
Here,
50% of n(U) = n(C ∩ M)
Or, 0.5 x n(U) = 550
∴ n(U) = 550/0.5 = 1100
Again, from the venn diagram above, we get
no(C) = (70% - x%) of n(U)
= (70% - 50%) x 1100
= 20% x 1100
= 0.2 x 1100
= 220
∴ Total number of people participated in survey = 1100 and the number of people who like curd only are 220.