A) 12
B) 18
C) 24
D) 36
Correct Answer: C
Solution :
Let there be x blue balls in the bag. \[\therefore \]Total number of balls in the bag \[=\left( \text{ }8\text{ }+\text{ }x \right)\]and Now, \[{{P}_{1}}\]= Probability of drawing a blue ball \[=\frac{x}{8+x}\]and \[{{P}_{2}}\]= Probability of drawing a red ball \[=\frac{8}{8+x}\] It is given that, \[{{P}_{1}}=3{{P}_{2}}\] \[\Rightarrow \,\,\,\,\,\frac{x}{8+x}=3\times \frac{8}{\left( 8+x \right)}\] \[\Rightarrow \,\,\,\frac{x}{8+x}=\frac{24}{8+x}\] Hence, there are 24 blue balls in the bag.
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