​Four persons 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?​

Correct option is D

Solution:

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".