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A box contains 24 balls of which some are yellow in color. If 12 more yellow balls are put in the box and a ball are drawn at random, the probability of drawing a yellow ball doubles that what it was before. Find the number of yellow balls in the box initially.

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10 Balls

5 Balls

17 Balls

6 Balls

answer is D.

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Detailed Solution

Let us assume that the number of yellow balls as x. Now, let us assume that the probability of getting a yellow ball from a box of 24 balls as P1.

P_{1} = \frac{x}{24}

Given that 12 more yellow balls are added to the box.
Now the total number of balls is 24+12=36 and the number of yellow balls is x+12.
Let us assume that the probability of getting a yellow ball now as P2.

P_{2} = \frac{x + 12}{36}

Also, P2 = 2P1

\Rightarrow \frac{x + 12}{36} = 2 \times \frac{x}{24}

\Rightarrow x + 12 = 3 x

\Rightarrow 2 x = 12

\Rightarrow x = 6

Hence, Option (4) is the correct answer.

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