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In a survey related to United Nation Security Council, 58% of those asked were in favour of at least one of the proposals I, II and III. 60% of those asked favoured proposal I, 25% of them favoured proposal II, and 15% of them favoured proposal III. If 4% of them favoured all three proposals, then what percentage of those asked favoured more than one of the three proposals?

In a survey related to United Nation Security Council, 58% of those asked were in favour of at least one of the proposals I, II and III. 60% of those asked favoured proposal I, 25% of them favoured proposal II, and 15% of them favoured proposal III. If 4% of them favoured all three proposals, then what percentage of those asked favoured more than one of the three proposals? Correct Answer 38%

Calculation:

⇒ Let the total number of people surveyed be 100.

⇒ Number of people in favour of at least one proposal = 58

From Venn diagram:

⇒ Number of people in favour of exactly two proposals = x + y + z

⇒ Number of people in favour of all three proposals = 4

⇒ Number of people in favour of only proposal I = 60 - (x + y + 4)

⇒ Number of people in favour of only proposal II = 25 - (x + z + 4)

⇒ Number of people in favour of only proposal III = 15 - (y + z + 4)

According to the question:

⇒ 58 = 60 - (x + y + 4) + 25 - (x + z + 4) + 15 - (y + z + 4) + (x + y + z) + (4)

⇒ 58 = 100 - (x + y + z) - 8

⇒ (x + y + z) = 34

⇒ Number of people who favoured more than one proposal = Number of people in favour of exactly two proposals + Number of people in favour of all three proposals

⇒ x + y + z + 4

⇒ 34 + 5 = 38

⇒ Required percentage = 38%

Additional Information

Three Overlapping Sets Region

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