UPSC Exam > UPSC Questions > A, B, C, D and E play a game of cards. A says...
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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 ?
- a)28
- b)29
- c)31
- d)35
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A, B, C, D and E play a game of cards. A says to B, "If you give ...
Understanding the Problem
To determine how many cards C has, we need to establish equations based on the information given.
Let’s Define Variables
- Let A, B, C, D, and E represent the number of cards each player has.
- The total number of cards is 150:
A + B + C + D + E = 150
From A's Statement
1. If B gives A 3 cards:
A + 3 = B - 3
This implies:
B = A + 6
2. If D takes 5 cards from B:
D + 5 = E
This implies:
E = D + 5
Relationship Between A, C, and E
- A and C together have twice as many cards as E:
A + C = 2E
By substituting E:
A + C = 2(D + 5)
A + C = 2D + 10
Equality Between B&D and A&C
- B and D together have the same number of cards as A and C:
B + D = A + C
Substituting B from earlier:
(A + 6) + D = A + C
This simplifies to:
D = C - 6
Substituting Values
Now, substitute D in the earlier equations:
- From E = D + 5, we have:
E = (C - 6) + 5 = C - 1
Now, substitute E into A + C = 2E:
- A + C = 2(C - 1)
- A + C = 2C - 2
- A = C - 2
Final Calculation
Substituting A, B, D, and E in the total equation:
A + (A + 6) + C + (C - 6) + (C - 1) = 150
This gives:
2A + 3C - 1 = 150
2A + 3C = 151
Using A = C - 2:
2(C - 2) + 3C = 151
2C - 4 + 3C = 151
5C = 155
C = 31
Thus, the number of cards C has is 31, confirming that the correct answer is option 'A'.
To determine how many cards C has, we need to establish equations based on the information given.
Let’s Define Variables
- Let A, B, C, D, and E represent the number of cards each player has.
- The total number of cards is 150:
A + B + C + D + E = 150
From A's Statement
1. If B gives A 3 cards:
A + 3 = B - 3
This implies:
B = A + 6
2. If D takes 5 cards from B:
D + 5 = E
This implies:
E = D + 5
Relationship Between A, C, and E
- A and C together have twice as many cards as E:
A + C = 2E
By substituting E:
A + C = 2(D + 5)
A + C = 2D + 10
Equality Between B&D and A&C
- B and D together have the same number of cards as A and C:
B + D = A + C
Substituting B from earlier:
(A + 6) + D = A + C
This simplifies to:
D = C - 6
Substituting Values
Now, substitute D in the earlier equations:
- From E = D + 5, we have:
E = (C - 6) + 5 = C - 1
Now, substitute E into A + C = 2E:
- A + C = 2(C - 1)
- A + C = 2C - 2
- A = C - 2
Final Calculation
Substituting A, B, D, and E in the total equation:
A + (A + 6) + C + (C - 6) + (C - 1) = 150
This gives:
2A + 3C - 1 = 150
2A + 3C = 151
Using A = C - 2:
2(C - 2) + 3C = 151
2C - 4 + 3C = 151
5C = 155
C = 31
Thus, the number of cards C has is 31, confirming that the correct answer is option 'A'.
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Community Answer
A, B, C, D and E play a game of cards. A says to B, "If you give ...
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.
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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 ?a)28b)29c)31d)35Correct answer is option 'A'. Can you explain this answer?
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