Answer
Verified
480.9k+ views
Hint- Total number of balls in the jar will be the sum of all colour balls. Consider some variable for the total number of balls, and then proceed further by the use of basic definition of probability.
Let the total number of balls in the given jar be $ = x$
As the probability of getting a red ball is $\dfrac{1}{4}$.
So total number of red ball in terms of variable $x$ is
$
= \dfrac{1}{4} \times x \\
= \dfrac{x}{4} \\
$
Also the probability of getting a blue ball is $\dfrac{1}{3}$ .
So total number of red ball in terms of variable $x$ is
$
= \dfrac{1}{3} \times x \\
= \dfrac{x}{3} \\
$
And the number of orange balls is $10$.
As we know that
Total number of balls in the jar = Number of red balls + Number of blue balls + Number of orange balls
$ \Rightarrow x = \dfrac{x}{4} + \dfrac{x}{3} + 10$
Taking LCM on the R.H.S. and then solving the algebraic equation.
$
\Rightarrow x = \dfrac{{4x + 3x + 120}}{{12}} \\
\Rightarrow 12x = 7x + 120 \\
\Rightarrow 5x = 120 \\
\Rightarrow x = 24 \\
$
Hence, the total number of balls in the jar is $24$ .
Note- Such a question as in above is easier to solve with the help of algebraic equations. Just we have to consider the unknown value as some variables and proceed. This problem can also be done in another way by first finding the probability of selection of orange balls by subtracting the sum of probabilities of red and blue balls from one and then comparing it with the number of orange balls.
Let the total number of balls in the given jar be $ = x$
As the probability of getting a red ball is $\dfrac{1}{4}$.
So total number of red ball in terms of variable $x$ is
$
= \dfrac{1}{4} \times x \\
= \dfrac{x}{4} \\
$
Also the probability of getting a blue ball is $\dfrac{1}{3}$ .
So total number of red ball in terms of variable $x$ is
$
= \dfrac{1}{3} \times x \\
= \dfrac{x}{3} \\
$
And the number of orange balls is $10$.
As we know that
Total number of balls in the jar = Number of red balls + Number of blue balls + Number of orange balls
$ \Rightarrow x = \dfrac{x}{4} + \dfrac{x}{3} + 10$
Taking LCM on the R.H.S. and then solving the algebraic equation.
$
\Rightarrow x = \dfrac{{4x + 3x + 120}}{{12}} \\
\Rightarrow 12x = 7x + 120 \\
\Rightarrow 5x = 120 \\
\Rightarrow x = 24 \\
$
Hence, the total number of balls in the jar is $24$ .
Note- Such a question as in above is easier to solve with the help of algebraic equations. Just we have to consider the unknown value as some variables and proceed. This problem can also be done in another way by first finding the probability of selection of orange balls by subtracting the sum of probabilities of red and blue balls from one and then comparing it with the number of orange balls.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE