Question

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 have together. If all together they have $150$ cards, how many cards has C got?

• A. $28$
• B. $29$
• C. $31$
• D. $35$

Answer 1

Answer: (A)

$28$

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: $C=28$.