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A bag contains $12$ balls of the two different colours out of which $x$ are white. One ball is drawn at random. If $6$ more white balls are put in a bag, the probability of drawing a white ball now will be doubled to that of previous probability of drawing a white ball. The value of $x$ is :

1. $4$
2. $5$
3. $6$
4. $3$

Option (D) is correct.

It is given that, total number of balls $=12$

Let the number of white balls $=x$

$\therefore$ Probability of getting a white ball = $\frac{x}{12}$

Now, $6$ white balls are added.  $\therefore$ Total number of balls $=12 + 6 = 18$

Number of white balls $= x + 6$

$\therefore$ Probability of getting a white ball $= \frac{x + 6}{18}$

According to the question,

\begin{align} \frac{x + 6}{18} &= 2 \times \frac{x}{12} \\ \implies x+6 &= 3x \\ \implies \quad ~ 2x &= 6 \\ \implies \quad ~~~ x&=3 \end{align}

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