Question

In a survey , it is found that 80 youngster's in a locality , liked only cricket . 45% of the youngsters liked only Foot ball . 5% of the youngsters liked both cricket and Foot ball . 10% of the youngsters liked neither cricket nor Foot ball . Then How many youngsters were surveyed in the locality ?

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Answer 1

Answer:

A total of 200 youngsters surveyed in the locality

Answer 2

160 youngsters were surveyed in the locality.

SOLUTION:

Given, In a survey , it is found that 80 youngster's in a locality , liked only cricket .

45% of the youngsters liked only Foot ball .  

5% of the youngsters liked both cricket and Foot ball .  

10% of the youngsters liked neither cricket nor Foot ball .  

Then we have to find How many youngsters were surveyed in the locality?

Let, the total number of youngsters surveyed be x.

We know that, total youngsters = youngsters who like games + youngsters who don’t like games.

x = youngsters who like games + 10% of x →  (1)

Now, youngsters who like games = youngsters who like only cricket + youngsters who only likes foot ball – youngsters who like both games.  [since, we know that, p(A U B) = p(A) + p(B) – p(A ∩ B)

youngsters who like games = 80 youngsters + 45% of x – 5% of x

Youngsters who like games = 80 + (45 – 5)% of x  

Youngsters who like games = 80 + 40% of x.

Substitute above value in (1)

x = 80 + 40% of x + 10% of x

= 80 + (40 + 10)% of x

= 80 + 50% × x

$\begin{array}{l}{x-\frac{50}{100} \times x=80} \\\\ {x\left(1-\frac{1}{2}\right)=80} \\\\ {x=2 \times 80=160}\end{array}$

Hence, 160 youngsters were surveyed in the locality.