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ICSE Class X Math 2013 Paper

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Question : 36 of 46
Marks: +1, -0
A box contains some black balls and 30 white balls. If the probability of drawing a black ball is two-fifths of a white ball, find the number of black balls in the box.
Solution:  
Let the number of black balls be xx, then
Total number of balls =30+x=30+x
Thus, the probability of black balls =x30+x=\frac{x}{30+x}
and the probability of white balls =3030+x=\frac{30}{30+x}
Given : Probability of black ball
=25× probability of white ball =\frac{2}{5} \times \text{ probability of white ball }
x30+x=25×30x+30\frac{x}{30+x} = \frac{2}{5} \times \frac{30}{x+30}
5x=605x = 60
x=12x = 12
Hence, the number of black balls =12=12.
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