In a survey 70% liked curd, 60% liked milk, 20% don’t like both curd and milk and 550 liked both curd and milk.

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,

1. n(U) = ?
2. n_o(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

n_o(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.