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# 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. - ICSE Class 10 - Mathematics

ConceptSimple Problems on Single Events

#### Question

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

Number of white balls in the bag = 30

Let the number of black balls in the box be x.

∴ Total number of balls = x + 30

P(drawing a black ball) = x/(x + 30)

P(drawing a white ball) = 30/(x + 30)

It is given that, P(drawing a black ball) = 2/5 xx P("drawing a white ball")

=> x/(x + 30) = 2/5 xx 30/(x + 30)

=> x/(x + 30) = 12/(x +  30)

=> x^2 + 30x = 12x + 360

=> x^2 + 18x - 360 = 0

=> x^2 + 30x -  12x - 360 = 0

=> x(x + 30) - 12(x + 30) = 0

=> (x + 30)(x - 12) = 0

=> x = -30 or x = 12

Since number of balls cannot be negative, we reject x = -30

=> x = 12

Therefore, number of black balls in the box is 12.

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Solution 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. Concept: Simple Problems on Single Events.
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