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
Solution(By Examveda Team)
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.
This Question Belongs to Competitive Reasoning >> Arithmetic Reasoning
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Comments ( 2 )
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Isn't the first condition should be A+3=B-3
And then the answer would be 31
As in question the statement says if B gives 3 to A it would be equal to A.
Let's take an example if A=20 and B =23 and here B gives its 3 to A then B will become 23-3=20 and A will become 20+3=23 and that's not equal, whereas taking another example if A=20 and B =26 and now B gives 3 to A then B becomes 26-3=23 and A becomes 20+3=23 and here A=B, si the exact difference between A and B should not be of 3 it should be off 6. Therefore the first condition should be A+3=B-3 => A=B-6.
Answer would be 31
As First condition is wrong.. which should be B-3 = A+3