# In a group of 75 people, 30 like cricket, 20 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

Latika Leekha
7 years ago
Let ‘C’ denote those who like cricket and let ‘T’ denote the people who like tennis.
Then, n(C) = 30.
n(C $\cap$ T) = 20.
The total number of people is given to be 75.
Hence, number of people who like cricket + those who like tennis – those who like both = 75.
(you can also prepare the venn diagram for the same)
Hence, n(C) + n(T) – n(C $\cap$ T) = 75.
30 + n(T) – 20 = 75.
This gives n(T) = 65.
Hence, 65 peolpe like tennis.
Now number of people who like only tennis and not cricket is given by
n(T) – n(C $\cap$ T) = 65 – 20
= 45.
Thanks & Regards
Latika Leekha
Latika Leekha
7 years ago
Let us assume that x people like tennis.
Number of people who like cricket = N(C) = 30.
The total number of people = 75.
Hence, using the venn diagram we have,
n(C) + n(T) – n(C $\cap$ T) = 75.
30 + x – 20 = 75.
Hence x = 65.
Those who like only tennis = x – n(C $\cap$ T)
= 65 – 20
= 45.
Thanks & Regards
Latika Leekha