Question

In a bag of marbles,$\dfrac{1}{2}$ of the marbles are red,$\dfrac{1}{4}$ of them are green, and $\dfrac{1}{5}$ of them are blue. If the remaining $2$ marbles are white, what is the no. of green marbles in the bag?
a. $4$
b. $5$
c. $8$
d. $10$
e. $40$

Answer 1

Hint: In this question we know the proportion in which every colored marble is present, so by assuming the total no. of marbles as $x$, we can calculate the no. of marbles of each and every color. After that as we know from the question that No. of white marbles is $2$, so by that we can find the value of $x$ from the equation
Total no. of marbles$ = $
 No. of red marbles $ + $No. of green marbles$ + $ No. of blue marbles$ + $ No. of white marbles
After finding the value of $x$, we can find the no. of green marbles from the given information about no. of green marbles.

Complete step-by-step answer: Here in this question we will start solving it after enlisting the given information first.
So, firstly in this question it is given that
In a bag of marbles
$\dfrac{1}{2}$of the marbles are red
$\dfrac{1}{4}$of them are green and$\dfrac{1}{5}$of them are blue
The remaining $2$marbles are white.
Now firstly, let us assume that total no. of marbles in the bag$ = x$
So, from the given information we can say that
No. of red marbles$ = \dfrac{1}{2}$of$x$
No. of red marbles$ = \dfrac{1}{2}x$
No. of green marbles$ = \dfrac{1}{4}$of$x$
No. of green marbles$ = \dfrac{1}{4}x$
No. of blue marbles$ = \dfrac{1}{5}$ of $x$
No. of blue marbles$ = \dfrac{1}{5}x$
So, as per question we know that there are four colored marbles i.e, Red, Green, Blue, White.
So, we can say that
Total no. of marbles$ = $
 No. of red marbles $ + $No. of green marbles$ + $ No. of blue marbles$ + $ No. of white marbles
So, we can say that if we subtract no. of green marbles, no. of red marbles, no. of blue marbles from total no. of marbles then we’ll get the no. of white marbles.
It means that
No. of white marbles$ = $
(Total no. of marbles)$ - $( No. of red marbles $ + $No. of green marbles$ + $ No. of blue marbles)
Now as we know
$ \Rightarrow $ No. of white marbles$ = x - \left( {\dfrac{1}{2}x + \dfrac{1}{4}x + \dfrac{1}{5}x} \right)$
$ \Rightarrow $ No. of white marbles$ = x - \left( {\dfrac{{10x + 5x + 4x}}{{20}}} \right)$
$ \Rightarrow $ No. of white marbles$ = x - \left( {\dfrac{{19x}}{{20}}} \right)$
$ \Rightarrow $ No. of white marbles$ = \dfrac{{20x - 19x}}{{20x}}$
$ \Rightarrow $ No. of white marbles$ = \dfrac{x}{{20}}$ ………(i)
Now, as we know that from the given information that
No. of white marbles$ = 2$
So, from equation (i) we can say that
$ \Rightarrow $ No. of white marbles$ = \dfrac{x}{{20}} = 2$
$ \Rightarrow x = 2 \times 20$
$ \Rightarrow x = 40$
$ \Rightarrow $Total no. of students is equal to$40$
So, as we know from the question that
No. of green marbles$ = \dfrac{1}{4}x$
$ \Rightarrow $ No. of green marbles$ = \dfrac{1}{4}\left( {40} \right)$
$ \Rightarrow $ No. of green marbles$ = 10$
So, our answer is $10$marbles are green.

Note: The alternative way of doing this question by finding the probability of white marbles, as we know the probability of each and every color of marbles except White color, so we can find the probability of white marbles by subtracting these given probabilities from total probability (or$1$).After that as we know the no. of white marbles and we have derived their probability, so we can find the total no. of marbles by the formula
$P$(White) $ = $(No. of white marbles) $ \div $(Total No. of marbles) .
And by that we can find the no. of Green marbles.