Question

A box contains 12 balls of which some are red in colour. If 6 more red balls are put in
the box and a ball is drawn at random, the probability of drawing a red ball doubles
than what it was before. Find the number of red balls in the bag.

Answer 1

Solution :-

Let the total number of red balls initially be x

Total number of balls in the box = 12

P(getting a red ball) = x/12

Now, 6 red balls are put in the box, then the total number of balls

= 12 + 6 

= 18 balls

Then total number of red balls = (x + 6)

Now,

P(getting a red ball) = (x + 6)/18

According to the question.

2(x/12) = (x + 6)/18

2x/12 = (x + 6)/18

Cross multiplying

⇒ 36x = 12x + 72

⇒ 36x - 12x = 72

⇒ 24x = 72

x = 3

So, initially the number of red balls in the box were 3 

Answer.

Answer 2

Total number of ball = 12

let number of red balls be = x

Hence P (red ball)=x/12

If 6 more balls are added , total number of balls = 12+6 = 18

Hence the number of red ball = x+6

P(red ball)= x+6/18

as per the question ,

x+6/18=2*[x/12]

x+6/18=x/6

6x+36=18x

x=3