question_answer

Suppose \[{{A}_{1}},{{A}_{2}}.....,{{A}_{30}}\]are thirty sets each  with five elements and \[{{B}_{1}},{{B}_{2}}.....,{{B}_{n}}\] are 'n' sets each with three elements. Let     \[\underset{i=1}{\mathop{\overset{30}{\mathop{\cup }}\,}}\,\,\,{{A}_{i}}=\underset{j=1}{\mathop{\overset{n}{\mathop{\cup }}\,}}\,\,\,\,{{B}_{j}}=S.\] Assume that each element of S belongs to exactly 10 of \[{{A}_{i}}s\] and exactly 9 of \[{{B}_{j}}s,\]then the value of x is

A)  \[90\]                  

B)  \[15\]

C)  \[9\]                 

D)  45