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?

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

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.

Suggest Corrections

Similar questions

$A, B, C, D$ 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?

Q. A, B, C, D and E play 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 ?

Q. 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?

Q. a , b, c, d and e are playing cards. In the game:
A says to B, If u give me three cards, u will have as many as E has and if I give u three cards, u will have as many as D has. A has three times the cards C has. If D has five cards more than what A has and the total no. of cards be 123.
1) How many cards does B have?
2) How many cards everyone has?
3) Explain the whole que, by writing the equ.

Q. A, B, C, D, and E play a game of cards. B has 6 cards less than E and A has 6 cards less than D. A and B together have a third of the number of cards D and E have. If B has two cards less than what C has and the total number of cards is 30, how many cards does B have?

Join BYJU'S Learning Program