Question

In a survey, it was found that 80% people liked oranges, 85% liked mangoes and 75% liked both but 45 people liked none of them. By drawing a venn diagram . Find the number of people who were in the survey .

Answer 1

Given : In a survey, it was found that 80% people liked oranges, 85% liked mangoes and 75% liked both but 45 people liked none of them.

To find : By drawing Venn diagram, find the no of people who were in the survey.

solution : see Venn diagram,

let O be the no of people who like oranges and M be the no of people who like mangoes.

let n(U) is the total no of people who were present in survey. i.e., n(U) = 100 %

now n(O u M) = n(O) + n(M) - n(O n M)

= 80% + 85% - 75%

= 90%

so, n(U) = n(O u M) + n'(O u M)

⇒100% = 90% + n'(O u M)

⇒10 % = n'(O u M)

here n'(O u M) is the set of no of people who like none of them.

but n'(O u M) = 45 = 10%

so, 100% = 450

Therefore 450 people were present in the survey.

Answer 2

Answer:

Answer is 450

Step-by-step explanation:

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