Answer

Verified

452.4k+ 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

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference Between Plant Cell and Animal Cell

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Change the following sentences into negative and interrogative class 10 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE