# Problem involving two sets

﻿Set

﻿Problems related to two sets

﻿﻿Q. In a survey of community, it was found that 70% liked curd, 60% liked milk, 20% didn't like both and 550 people liked both curd and milk. Then,

• Find the total no. of people participated in the survey

• Find the total no. of people who like only curd

• Represent it in venn-diagram.

Solution:

Let U, C and M represents the set of total people in survey, people who like curd and milk respectively.

Given:   n(C)=70%                n(M)=60%                     n(C∪M)'=20%         n(U)=100%
﻿n(﻿C∩M)=550
﻿We know,

n(C∪M)= n(U) - n(C∪M)'

= 100% - 20%

= 80%

And,   (C∩M) = n(C)+ n(M)- n(C∪M)

=70%+ 60%- 80%

= 50%

Let the total no. of people in the survey be x.

According to the question,

50% of x = 550

or, (50/100)*x = 550

or, 0.5 x = 550

or, x = 550/0.5

or, x = 1100

• Therefore, the total no. of people in tge survey is 1100.

Now,  n०(C)= n(C) -n(C∩M)        [०=only]

=70%-50%

=20%

Then,  20%of 110=(20/100)*1100= 22

• So, 220 poeple in the survey liked curd only.

Venn-diagram: