Suppose A1,A2,…,A30 are thirty sets each having 5 elements and B1,B2,…,Bn are n sets each with 3 elements.  Let ∪i=130 Ai=∪i=1n Bj=S and each element of S belongs to  exactly 10 of the Ai 's and exactly 9 of the Bj 's.  Then n is equal to

If elements are not repeated, then number of elements in  A1∪A2∪A3,…∪A30 is 30×5 But each element is used 10 times, so S=30×510=15 If elements in B1,B2,…,Bn , are not repeated, then total number  of elements is 3n . But each element is repeated 9 times, so S=3n9⇒15=3n9⇒n=45