Question

A, B, C, D and E play a game of cards. A says to B, "If you give me 3 cards, you will have as many as I have at this moment while if D takes 5 cards from you, he will have as many as E has". A and C together have twice as many cards as E has. B and D together also have the same number of cards as A and C taken together. If together they have 150 cards, then how many cards has C got?

• A. 28
• B. 29
• C. 31
• D. 35

Answer 1

The correct option is A 28

The solution for the problem is:

(1) A = B - 3

(2) D + 5 = E

(3) A+C = 2E

(4) B + D = A+C = 2E

(5) A+B + C + D + E=150

From (3), (4) and (5), we get: 5E = 150 or E = 30.

Putting E = 30 in (2), we get: D = 25.

Putting E = 30 and D = 25 in (4), we get: B = 35.

Putting B = 35 in (1), we get: A = 32.

Putting A = 32 and E = 30 in (3), we get: C = 28.