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.

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Solution

Given : Total population $(ξ) = 2500$
No of people use brand A $= n (A) = 1300$
No of people use brand B $= n (B) = 1050$
No of people who use both the brands $= n (A \cap B) = 250$
No of people who use either of the brands $= n (A \cup B)$
Now, $n (A \cup B) = n (A) + n (B) - n (A \cap B)$
$= 1300 + 1050 - 250 = 2100$
No of people who use neither of the soaps $= n (A \cup B)^{'} = ξ - n (A \cup B) = 2500 - 2100 = 400$
$%$ of population who use neither of these soaps $= \frac{400}{2500} \times 100 = 16 %$

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