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Three sisters $(R, S,$ and $T)$ received a total of $24$ toys during Christmas. The toys were initially divided among them in a certain proportion. Subsequently, $R$ gave some toys to $S$ which doubled the share of $S$. Then $S$ in turn gave some of her toys to $T$, which doubled $T’$s share. Next, some of $T’$s toys were given to $R$, which doubled the number of toys that $R$ currently had. As a result of all such exchanges, the three sisters were left with equal number of toys. How many toys did $R$ have originally?

  1. $8$
  2. $9$
  3. $11$
  4. $12$
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We can proceed in reverse order:

$R\quad  S\quad  T$
$8\quad  8\quad   8$

and apply the given steps in reverse. We will get,

$R\quad  S\quad  T$
$4 \quad 8 \quad 12$
$4 \quad 14 \quad 6$
$11  \quad 7 \quad  6$

Correct Answer: $C$
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