Let the sets A = 2 , 4 , 6,8 … and B = 3 , 6 , 9 , 12 … such that n A = 200 and n B = 250. If n A ∪ B = k , then k 100 is equal to

Step-by-step solution

Let, the last element of set A is, t 200 = 2 + 200 - 1 2 = 400 and the last element of set B is t 250 = 3 + 250 - 1 3 = 750 Common elements are → 6 , 12 , 18 … We have to find the common elements upto 400 t n = 6 + n - 1 6 ⇒ 400 = 6 + 6 n - 6 ⇒ n = 400 6 = 66.6 … t 66 = 6 + 66 - 1 6 = 396 Number of common elements = 66 n A ∪ B = n A + n B - n A ∩ B = 200 + 250 - 66 = 384 ⇒ k = 38 4 ⇒ k 100 = 3.84