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, how many cards has C got ?

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, how many cards has C got ?
[A].

28

[B].

29

[C].

31

[D].

35

Answer: Option A

Explanation:

Clearly, we have :

A = B – 3 …(i)

D + 5 = E …(ii)

A+C = 2E …(iii)

B + D = A+C = 2E …(iv)

A+B + C + D + E=150 …(v)

From (iii), (iv) and (v), we get: 5E = 150 or E = 30.

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

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

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

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