A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball? If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find x.

Total number of balls = 12
Total number of black balls = x
P (getting a black ball) = x/12
If 6 more black balls are put in the box, then
Total number of balls = 12 + 6 = 18
Total number of black balls = x + 6
P (getting a black ball now) = (x + 6)/18
According to the condition given in the question,
2(x/12) = (x + 6)/18
⇒ 3x = x + 6
⇒ 2x = 6
⇒ x = 3

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