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  4. In a city, 20 percent of the population travels by car, 50 percent by bus and 10 percent travels by both car and bus. Then person travelling by car or bus is

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Q. In a city, $20$ percent of the population travels by car, $50$ percent by bus and $10$ percent travels by both car and bus. Then person travelling by car or bus is

Sets

Solution:

Let population be $100$. Let $A$ and $B$ be the sets consisting of population which travels by car and by bus respectively.
$n(A) = 20$, $n(B) = 50$ and $n(B \cap A) = 10$
$n(A \cup B) = n(A) + n(B) - n(A \cap B)$
$= 20 + 50 - 10 = 60\%$.