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?

• A. 22
• B. 23
• C. 25
• D. 35

Hint:

In complex word problems, convert each statement into equations step-by-step and reduce variables systematically—trial with options can speed up the final step.

Answer 1

The Correct Option is C

Concept: This is a system of linear equations involving redistribution of cards among five people, where relationships between their card counts are given. Step 1:Define variables and translate conditions.
Let cards with A, B, C, D, E be a, b, c, d, e. From the given relations:

• a + 3 = e
• b + 3 = d
• a + b = d + e + 10
• b = c + 2
• a + b + c + d + e = 133

Step 2:Rewrite variables using substitutions.
From b = c + 2 ⇒ c = b − 2
From b + 3 = d ⇒ d = b + 3
From a + 3 = e ⇒ e = a + 3 Substitute into total: \[ a + b + (b-2) + (b+3) + (a+3) = 133 \] Simplify: \[ 2a + 3b + 4 = 133 \Rightarrow 2a + 3b = 129 \]
Step 3:Find integer solution satisfying consistency.
Test values satisfying 2a + 3b = 129: Let b = 25: \[ 2a + 75 = 129 \Rightarrow 2a = 54 \Rightarrow a = 27 \] Now compute others:

• c = 23
• d = 28
• e = 30

Check sum: \[ 27 + 25 + 23 + 28 + 30 = 133 \]