Question

The probability of selecting a green marble at random from a jar that contains only green, white and yellow marbles is $\frac{1}{4}$. The probability of selecting a white marble at random from the same jar is $\frac{1}{3}$. If this jar contains $10$ yellow marbles. What is the total number of marbles in the jar?

• A. $20$
• B. $24$
• C. $35$
• D. $40$

Answer 1

The correct option is B $24$

$P$(Green marble) $=\frac{1}{4}$
$P$(white marble) $=\frac{1}{3}$
Let number of green marble $= x$
and number of white marble $=y$
So, $P$(Green marble) $=\frac{x}{x+y+10}$
$\therefore \frac{x}{x+y+10}=\frac{1}{4}$
$4x=x+y+10$
$3x-y=10$ ........ (i)
$P$(Green marble) $=\frac{x}{x+y+10}$
$\therefore \frac{x}{x+y+10}=\frac{1}{3}$
$x+y+10=3y$
$-x+2y=10$ ........ (ii)
Multiply equation (i) by (ii)
$6x-2y=20$
$-x+2y=10$
------------------------------
$5x=30$
$x=6$
substitute $x=6$ in equation (i)
$3\times 6-y=10$
$y=8$
So, total number of marbles $=x+y+10$
$=6+8+10$
$=24$