Question

in a group of 65 people,40 people like cricket,10 people like both cricket and tennis.how many like tennis Only and not cricket?how many like tennis?​

Answer 1

Answer:

35 people like tennis

Step-by-step explanation: 40 like cricket but 10 like both tennis & cricket.

So, 30 like only cricket.

So, 65-30=35 like tennis and 25 only like tennis

Answer 2

$\Large{\underline{\underline{\bf{Solution :}}}}$

☯ Given :

• There are total 65 People in a group n(AUB).
• People like cricket n(A) = 40
• People like both cricket and tennis (A∩B) = 10.

$\rule{200}{1}$

☯ To Find :

We have to find the people who like only tennis and people who like tennis.

$\rule{200}{1}$

☯ Explanation :

We know that,

$\large{\implies{\boxed{\boxed{\sf{n(AUB) = n(A) + n(B) - n(A \cap B)}}}}}$

→ Putting Values in above formula

$\sf{\rightarrow 65 = 40 + n(B) - 10} \\ \\ \sf{\rightarrow 65 = 30 + n(B)} \\ \\ \sf{\rightarrow n(B) = 65 - 30} \\ \\ \sf{\rightarrow n(B) = 35} \\ \\ \Large{\implies{\boxed{\boxed{\sf{n(B) = 35}}}}} \\ \\ \sf{\therefore \: 35 \: people \: like \: tennis}$

$\rule{200}{2}$

Now,

We will find people who only like tennis.

We know that,

$\large{\implies{\boxed{\boxed{\sf{Only \: tennis = n(B) - n(A \cap B)}}}}}$

→ Put Value in the above given formula

$\sf{\rightarrow Only \: tennis = 35 - 10} \\ \\ \sf{\rightarrow Only \: tennis = 25} \\ \\ \Large{\implies{\boxed{\boxed{\sf{Only \: tennis = 25}}}}} \\ \\ \sf{\therefore \: 25 \: people \: like \: only \: tennis}$