Question

Suppose A₁, A₂, ...., A₃₀ are thirty sets each having 5 elements and B₁, B₂, ..., B_n are n sets each with 3 elements. If 

and each element of S belongs to exactly 10 of A_i 's and to exactly 9 of B_j 's. then n is equal to

(A) 35 

(B) 3 

(C) 15 

(D) 45

Answer 1

Correct option (D) 45

Explanation:

(30 x 5)/10 = (n x 3)/9

⇒ n = 45