Question

In a group of 250 boys, 60% like Hindi films, 70% like English films & 50% like both. Howmany of
them donot like any of these films?
1) 25
2) 40
3) 50
4) 60
5) None of these​

Answer 1

Answer:

Total Boys=250

n(A ∪ B) = n(A) + n(B) - n(A∩B)

50%= 70%+ 50%  - n(A∩B)

Therefore, n(A∩B)= 70%

Percentage of those who do not like both film = 100-70= 30%

No. of person who do not like both film = 30% of 250 = 75

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Answer 2

Given:

A group of 250 boys.

60% like Hindi films,

70% like English films,

50% like both Hindi and English films.

To find:

How many of  them do not like any of these films.

Formula to be used:

n(A ∪ B) = n(A) + n(B) - n(A∩B)

Solution:

Total number of boys = 250

We can find the number of boys who don't like any of the films by using the following formula,

n(A ∪ B) = n(A) + n(B) - n(A∩B)

60% like Hindi films, n(A) = 60%

70% like English films, n(B) = 70%

50% like both Hindi and English films, n(A∩B) = 50%

Therefore,

n(A ∪ B) = 60% + 70% - 50%

n(A ∪ B) = 130% - 50%

n(A ∪ B) = 80%

Therefore,

Percentage of those who do not like both film is 100 - 80 = 20%

Number of boys who do not like both film is 20% of 250 = $\frac{20}{100}$ × 250

Number of boys who do not like both film = 50

Final answer:

50 boys do not like any of these films.

Thus, the correct option is 3) 50