Q17 of 71 Page 30

A village has total population of 2500 people. Out of which 1300 people use brand A soap and 1050 people use brand B soap and 250 people use both brands. Find the percentage of population who use neither of these soaps.

Given


total population n(U) = 2500


no of people use brand A soap n(A) = 1300


no of people using brand B soap n(B) = 1050


no people using both brand n(A∩B) = 250


We know that


n(A∪B) = n(A) + n(B) – n(A∩B)


= 1300 + 1050–250


= 2100


n(A∪B)' = n(U) – n(A∪B)


= 2500–2100


= 400


Percentage of population who use neither of these soaps


= (400/2500)x100


= 0.16 x 100


= 16%


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The following table shows the percentage of the students of a school who participated in Elocution and Drawing competitions.


Draw a Venn diagram to represent this information and use it to find the percentage of the students who


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iii. did not participate in any one of the competitions.

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