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Question

A, B, C, and D are playing a game of cards. A says to B, "If you give me 4 cards, you will have twice as much as C. If you give me 3 cards, you will have 10 more cards than D." The total number of cards C and D have is 31. How many cards does B have?

A
11
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B
21
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C
30
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D
34
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Solution

The correct option is D 34
Given:
If B gives 4 cards to A, B will have thrice the number of cards present with C.

So,

B – 4 = 3C ---------------- (1)

If B gives 3 cards to A, B will have 10 cards more than D.

Hence, we have,

B – 3 = D + 10 -------------- (2)

Total number of cards with C and D = 31

So,

C + D = 31 ------------------ (3)

On subtracting equation (2) from equation (1), we get,

3C – (D + 10) = (B – 4) – (B – 3)
⇒ 3C – D – 10 = –1
⇒ 3C – D = 9

On substituting equation (3) in the given equation, we get,

3C – (31 – C) = 9

⇒ 4C – 31 = 9

⇒ 4C = 40

⇒ C = 10

On substituting this value in equation (1), we get,

B – 4 = 3C

⇒ B = 3C + 4

⇒ B = 3(10) + 4

⇒ B = 30 + 4 = 34

Hence, B will have 34 cards.

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