In a group of 100 people, 50 people like to eat chicken and 25 people like to eat both chicken and mutton. Everyone in the group like at least one of the two. How many people like only mutton?

In a group of 100 people, 50 people like to eat chicken and 25 people like to eat both chicken and mutton. Everyone in the group like at least one of the two. How many people like only mutton? Correct Answer 50

Given:

Total people in group = 100

Like only chicken = 50

Like both = 25

Formula used:

n(A∪B) = n(A) + n(B) − n(A∩B)

Only B for

n(B − A) = n(B) − n(B∩A)

Calculation:

Let A denote the set the people like chicken, and B denote the set of people who like mutton

Here, n(A∪B) = 100, n(A) = 50, n(A∩B) = 25

n(A∪B) = n(A) + n(B) − n(A∩B)

⇒ 100 = 50 + n(B) − 25

⇒ 100 = 25 + n(B)

⇒ n(B) = 100 – 25

⇒ n(B) = 75

Then 75 people like Mutton

According to question,

n(B − A) = n(B) − n(B∩A)

⇒ n(B − A) = 75 – 25

⇒ n(B − A) = 50

∴ 50 people like only mutton.

Shortcut Trick

Venn diagram

[ alt="F1 Shraddha Ujjwal 28.05.2021 D3" src="//storage.googleapis.com/tb-img/production/21/05/F1_Shraddha_Ujjwal_28.05.2021_D3.png" style="width: 321px; height: 154px;">

According to venn diagram 

⇒ 25 people like only chicken

⇒ 25 people like both

⇒ 50 people like only mutton

∴ 50 people like only mutton.