A bag contains, white, black and red balls only. A ball is drawn at random from the bag. If the probabilityof getting a white ball is and that of a black ball is , then find the probability of getting a red ball. If thebag contains 20 black balls, then find the total number of balls in the bag
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Let the no of white balls be = x
Let the no of red balls be = y
number of balls black balls =20
total number of balls =x+y+20
Probability of getting a white ball =3/10
x/x+y+20=3/10
=> 10x=3x+3y+60
=> 7x−3y=60------(1)
Probability of getting a blind ball =2/5
(i.e)20x+y+20=25
= 100=2x+2y+40
=> 2x+2y=60
or x=y=30 ----------(2)
Solving (1) and (2) we get,
7x−3y=60
x+y=30
______________
7x−3y=60
7x+7y=210
________________
−10y=150
=> y=15
x=15
Answer : 15
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