Suppose $A_1 , A_2,... A_{30}$ are thirty sets each having 5 elements and $B_1, B_2,..., B_n$ are n sets each with 3 elements , let $\underset{i = 1}{\overset{30}{\cup}} A_i = \underset{j = 1}{\overset{n}{\cup}} B_j = S$ and each element of S belongs to exactly 10 of the $A_i's$ and exactly 9 of the $B_j'S$. then n is equal to

If elements are not repeated then the number of elements in $A_1\cup A_2\cup A_3\cup A_{30}$ is $30\times 5$

But each elements is used 10 times

so, $S=\cfrac{30\times 5}{10}=15$

If the elements in $B_1,B_2,.....,B_n$ are not repeated.

then total number of element in

$B_1\cup B_2\cup B_3.....\cup B_n$ is 3n

but each elements is repeated 9 times

so,

$S=\cfrac{3n}{9}=15=\cfrac{3n}{9}$

$n=45$