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

Question

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 (A) 80 % (B) 40 % (C) 60 % (D) 70 %

Tardigrade Admin · Accepted Answer

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 ∩ A) = 10 n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 20 + 50 - 10 = 60 %.

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

$80%$

$40%$

$60%$

$70%$

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 $n (B \cap A) = 10$
$n (A \cup B) = n (A) + n (B) - n (A \cap B)$
$= 20 + 50 - 10 = 60%$ .

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

80%

40%

60%

70%