Answer

Verified

379.5k+ views

**Hint:**In order to find the number of persons in \[II\] group, we must be considering the variable values for both the groups. Then calculating the mean of both the groups as the total persons of both the groups is \[160\]. We must be equating this mean equation to \[Rs.430\]. And then on solving, we obtain the required answer.

**Complete step-by-step solution:**

Now let us learn about meaning. The mean of data is nothing but the average of the observations which means as the central value of the data. It is generally calculated by the sum of observations divided by the number of observations. Mean is a part of measures of central tendency. There are three types of mean. They are: Arithmetic mean, geometric mean and harmonic mean.

Now let us find the number of persons in group \[II\].

Let us consider the number of persons in group \[I\] is \[x\]

Let us consider the number of persons in group \[II\] as \[y\].

We are given that \[x+y=160\] \[\to \left( 1 \right)\]

So now let us calculate the income of both the groups.

Total income of group \[I\]is \[400x\]

Total income of group \[II\] is \[480y\].

We are given that mean income of both the groups is \[430\]

We can express this as

\[\Rightarrow \dfrac{400x+480y}{x+y}=430\]

Upon solving this, we get

\[\begin{align}

& \Rightarrow 400x+480y=430x+430y \\

& \Rightarrow 50y=30x \\

& \Rightarrow 50y-30x=0 \\

\end{align}\]

\[50y-30x=0\to \left( 2 \right)\]

Here we multiply the equation 1 with 30 and add to equation 2, so we get $\{30x+30y=4800\}+\{50y-30x=0\}$

$\Rightarrow 50y+30y=4800$

$\Rightarrow y=\dfrac{4800}{80}=60$

Now we substitute x=60 in equation 1, so we get

$60+y=160$ $\Rightarrow y=100$

Thus Upon solving the first and second equations, we get

\[\begin{align}

& x=100 \\

& y=60 \\

\end{align}\]

\[\therefore \] Number of persons in group \[II\] is \[60\]

**Hence, option C is the correct answer.**

**Note:**We must always calculate the values accurately for obtaining the accurate answers. In the problem above, we have considered variables for the unknown values and we must note that this method is applicable to all such problems. We can use mean in finding our marks, or calculating the total goods sold per day and many more.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Harsha Charita was written by A Kalidasa B Vishakhadatta class 7 social science CBSE

Which are the Top 10 Largest Countries of the World?

Banabhatta wrote Harshavardhanas biography What is class 6 social science CBSE

Difference Between Plant Cell and Animal Cell

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

How do you graph the function fx 4x class 9 maths CBSE

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

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE