Q20 of 46 Page 1

A bag contains, white, black and red balls only. A ball is drawn at random from the bag. If the probability of getting a white ball is 3/10 and that of a black ball is 2/5, then find the probability of getting a red ball. If the bag contains 20 black balls, then find the total number of balls in the bag.

Let the no of white balls = x


Let the no of red balls = y


No of black balls = 20 [given]


Total No of balls = x + y + 20




10x = 3x + 3y + 60


7x - 3y = 60 ….[1]



100 = 2x + 2y + 40


2y + 2x = 60


x + y = 30


x = 30 - y ….[2]


using [1] and [2]


7(30 - y) - 3y = 60


210 - 7y - 3y = 60


10y = 150


y = 15


No of red balls = 15


using this in eqn 2


x = 30 - 15 = 15


No of white balls = 15


Total no of balls : x + y + 20 = 15 + 15 + 20 = 50



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