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 gave 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?

Correct option is C

Step 1: Assign Variables

Let the number of cards each player has be as follows:

A has a cards.

B has b cards.

C has c cards.

D has d cards.

E has e cards.

Step 2: Set up Equations

1. From the first statement, we know that if B gives 3 cards to A, B will have as many cards as E:

b - e = 6(Equation 1)

2. From the second statement, we know that if A gives 3 cards to B, B will have as many cards as D:

b - d = -6(Equation 2)

3. From the third statement, A and B together have 10 cards more than D and E together:

a + b = d + e + 10(Equation 3)

4. From the fourth statement, B has two cards more than C:

b = c + 2(Equation 4)

5. The total number of cards is 133:

a + b + c + d + e = 133(Equation 5)

Step 3: Solve the System of Equations

From Equation 1, we have:

e = b - 6

From Equation 2, we have:

d = b + 6

From Equation 4, we have:

c = b - 2

Substitute these values into Equation 5 (Total Cards equation):

a + b + (b - 2) + (b + 6) + (b - 6) = 133

Simplifying the equation:

a + 4b - 2 = 133

a + 4b = 135(Equation 6)

Substitute e = b - 6 and d = b + 6 into Equation 3:

a + b = (b + 6) + (b - 6) + 10

Simplifying the equation:

a + b = 2b + 10

a = b + 10(Equation 7)

Substitute a = b + 10 into Equation 6:

b + 10 + 4b = 135

Simplifying:

5b + 10 = 135

5b = 125

b = 25

Final Answer:

The number of cards B has is 25.