A, B, C and D play a game of cards. A says to B, 'If I give you 8 cards, you will have as many as C has and I shall have 3 less than what C has. Also if I take 6 cards from C, I shall have twice as many as D has'. If B and D together have 50 cards, how many cards has A got?

As per the information,

• If A gives 8 cards to B then B will have as many as C has  and A will have 3 less than what C has:

⇒ B + 8 = C      ------- (i)

⇒ A - 8 = C - 3 or C = A - 5   ------ (ii)

• Also if A takes 6 cards from C, a will have twice as many as D has:

⇒ A + 6 = 2D   -------- (iii)

• And B and D together have 50 cards:

⇒ B + D = 50  or D = 50 - B  -------- (iv)

Now,

Putting (ii) into (i), we have:

⇒ B + 8 = A -  5 

⇒ A - B = 13   -------- (v)

⇒ A = 13 + B   ------  (a)

Putting (iv) into (iii), we have:

⇒ A + 6 = 2(50 - B)

⇒ A + 6 = 100 - 2B

⇒ A + 2B = 94   -------- (vi)

⇒ A = 94 - 2B   -------- (b)

Solving (a) and (b), we get:

⇒ 13 + B = 94 - 2B

⇒ 3B = 94 - 13

⇒ 3B = 81

⇒ B = 27

Putting value of (b) in (a), we get:

⇒ A = 13 + 27

⇒ A = 40

Thus, A got '40' cards.

Hence, the correct answer is "40".