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Q.

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 ?

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a

28

b

29

c

35

d

31

answer is A.

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Detailed Solution

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=l50 (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.

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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 ?