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Question

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 be 133, how many cards does B have?


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Solution

Finding the number of cards B have:

Let A,B,C,D and E have a,b,c,d and e number of cards respectively.

Now, 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.

b3=e……….(1)

b+3=d….. … (2)

A and B together have 10 cards more than what D and E together,

a+b=d+e+10 …….… (3)

B has two cards more than C,

b=c+2 ………………..… (4)

Total number of cards is 133,

a+b+c+d+e=133……..… (5)

From (1) and (2), we get,

b-e=d-b2b=d+e

2b=d+e……….. .. (6)

From (3) and (6)

a+b=2b+10b=a-10

a=b+10…………..(7)

From (4), (5), (6) and (7), we get,

a+b+c+d+e=133b+10+b+b-2+2b=1335b+8=1335b=133-85b=125b=25

Hence, B has 25 cards.


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