Question

in a Group of 65 people , 40 like cricket and 10 like both cricket and tennnis .How many people like tennis only and not cricket? How many like tennis

Answer 1

In Group of 65 people

Given

• 40 liked Cricket
• 10 liked both Cricket & Tennis

To Find

• How many liked tennis?
• How many people liked tennis but but not cricket?

Solution

Total People - Cricket Likers + Likers of Both Cricket & Tennis

Substituting Values

☞ 65-40+10

☞ 75-40

☞ 35

Therefore, 25 people liked Tennis

Calculating, people who liked tennis & not cricket

Thus,

Tennis likers - likers of both cricket & tennis

Substituting Values

☞ 35 - 10

☞ 25

Hence

Number of Tennis likers ➠ 35

Number of likers who liked tennis but not cricket ➠ 25

Answer 2

$\large\bf\green{ To \ Find:- }$

• we need to find that how many people like tennis only not cricket.

• how many people like tennis ?

$\huge\bf\purple{Solution:- }$

Let C be the set of people who plays cricket . and T be the set of people who plays tennis.

Total number of persons in a group = 65

So,

• n(T ∪ C) = 65

40 people like both tennis and cricket.

So,

• n(T) = 40

10 people like both tennis and cricket.

So,

• n(T ∩ C) = 10

• || By using Formula || :-

⇛《 n(T ∪ C) + n(T ∩ C) = n(T) + n(C) 》

⟶ n(T) = n(T ∪ C) + n(T ∩ C) - n(C)

⟶ n(T) = 65 + 10 - 40

⟶ n(T) = 75 - 40

$\longrightarrow \underline{\boxed{ \bf \red{n(T) = 35}}}$

So,

35 people like Tennis.

Now,

People who like only tennis not cricket are :-

⟶ n(T - C) = n(T) - n(T ∩ C)

⟶ n(T - C) = 35 - 10

⟶ n(T - C) = 25

So,

25 people like only tennis not cricket.

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