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

$\huge\boxed{\texttt{\fcolorbox{Red}{aqua}{Hey Mate!!!}}}$

Let the total number of red balls be x

Total number of balls in the box = 12

P(getting a red ball). = $\frac{x}{12}$

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

=12+6
=18 balls

Then,Total number of red balls. =(x+6)

Now,
P(getting a red ball). =$\frac{x+6}{18}$

ATQ,
$2( \frac{x}{12}) = \frac{(x + 6)}{18} \\ \frac{2x}{12} = \frac{(x + 6)}{18}$
By cross-multiplication
$30x = 12x + 72 \\ 30x - 12x = 72 \\ 24x = 72 \\ x = 3$
So, The number of red balls in the box is 3.

$\large{\red{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\underline{\underline{Hope\:it\:helps\: you}}}}}}}}}}}}}}$

Answer 2

$hello \: here \: is \: your \: answer \\ hello$
hello thanks for asking this question ☺☺☺


number of black balls = x

∴ number of favorable outcomes = x

total number of balls = 12

∴ total number of outcomes = 12

∴ P (black ball) =
$\frac{x + 6}{18}$


now 6 new black balls added

∴ number of black balls = x + 6

∴ number of favorable outcomes = x + 6

total number of balls = 12 + 6 = 18

∴ P (black ball) =
$\frac{x + 6}{18}$


according to the question

=
$\frac{x + 6}{18} = 2 \times \frac{x}{6}$


=
$\frac{x + 6}{18} = \frac{x}{6}$


6 (x + 6) = 18x

6x + 36 = 18x

36 = 18x - 6x

36 = 12x

3 = x