Each set X, contains 5 elements and each set Y, contains 2 elements and $⋃_{r = 2}^{20} X_{r} = S = ⋃_{r = 1}^{n} Y_{r}$ . If each element of S belongs to exactly 10 of the $X_{r}^{^{'} s}$ and to exactly 4 of $Y_{r}^{^{'} s}$ then find the value of n.

Q. Each set X_r contains 5 elements and each set Y_r contains 2 elements and

\cup_{r = 1}^{20} X_{r} = S = \cup_{r = 1}^{n} Y_{r}

. If each element of S belongs to exactly 10 of the

X_{r}^{' s}

and to exactly 4 of the

Y_{r}^{' s},

then n is
(a) 10
(b) 20
(c) 100
(d) 50

Suppose $A_{1}, A_{2}, . . . . . . . . . . . . . . . . . . . . ., A_{30}$ are thirty sets each having 5 elements each and $B_{1}, B_{2}, . . . . . . . . . . . . . . . . B_{n}$ are $n$ sets each with 3 elements each. Let $30 ⋃ i = 1 A_{i} = n ⋃ j = 1 B_{j} = S$ and each element of $S$ belongs to exactly 10 of $A_{i}$ 's and exactly 9 of the $B_{j}$ 's. Then $n$ is equal to

Q. Suppose

A_{1}, A_{2} . . . . . A_{30}

are thirty sets having 5 elements and

B_{1}, B_{2} . . . . B_{n}

are n sets each with 3 elements. Let

30 ⋃ i = 1 A i = n ⋃ i = 1 B j = S

and each elements of S belongs to exactly 10 of the Ai's and exactly 9 of the Bj's. Then n is equal to

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Let 50⋃i=1Xi=n⋃i=1Yi=T, where each Xi contains 10 elements and each Yi contains 5 elements. If each element of the set T is an element of exactly 20 of sets Xi's and exactly 6 of sets Yi's, then n is equal to

Let $50 ⋃ i = 1 X_{i} = n ⋃ i = 1 Y_{i} = T,$ where each $X_{i}$ contains $10$ elements and each $Y_{i}$ contains $5$ elements. If each element of the set $T$ is an element of exactly $20$ of sets $X_{i}$ 's and exactly $6$ of sets $Y_{i}$ 's, then $n$ is equal to