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.

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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 2

Answer:

let the number of red balls be 'x'

probability of drawing a red ball= (number of red balls/total number of balls)= x/12

now,

6 red balls are added to the box

so, number of red balls=x+6

now,

probability of red ball= (x+6/12)

Acc. to question,

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

therefore,

x= 6

hence, number of red balls =6