#### 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.