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A, B, C, D and E play a game of cards. A says to B, “If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has.” A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards is 133, how many cards does B have?

Options

  1. A22
  2. B23
  3. C25
  4. D35

Correct answer

C. 25

Step-by-step solution

According to the given information, B - 3 = E -------- ( 1 ) B + 3 = D ------- ( 2 ) A + B = D + E + 10 ----- ( 3 ) B = C + 2 -------- ( 4 ) A + B + C + D + E = 133 ------ ( 5 ) Now, if we add equations ( 1 ) and ( 2 ) , we get, 2 B = E + D -------- ( 6 ) Substituting equation ( 6 ) in ( 3 ) , A + B = 2 B + 10 A = B + 10 -------- ( 7 ) Substituting equations ( 4 ) ,   ( 6 ) and ( 7 ) , in equation ( 5 ) , we get, ( B + 10 )   +   B   +   ( B - 2 )   +   2 B = 133 5 B + 8 = 133 5 B

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