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. $35$

Answer 1

The correct option is C $25$

Clearly, we have :
$B-3=E$ .....(i)
$B+3=D$ .....(ii)
$A+B=D+E+10$ .....(iii)
$B=C+2$ ......(iv)
$A+B+C+D+E=133$ ......(v)
From (i) and (ii), we have : $2B=D+E$ .....(vi)
From (iii) and (vi), we have : $A=B+10$ ......(vii)
Using (iv), (vi) and (vii) in (v), we get
$(B+10)+B+(B-2)+2B=133\iff 5B=125\iff B=25$.