The average incomes of the people in two vill | vedclass

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Question

(C) Let the number of people in the two villages be $x$ and $y$ respectively.Given,the average income of $x$ people is $P$ and the average income of $

Vedclass · Accepted Answer

$P^{\prime} = P$ and $Q^{\prime} = Q$

Vedclass · Answer

(C) Let the number of people in the two villages be $x$ and $y$ respectively.Given,the average income of $x$ people is $P$ and the average income of $y$ people is $Q$.Therefore,the total income of people in the two villages is $Px$ and $Qy$ respectively.One person with income $I$ moves from the first village to the second village.Then,the number of people in the first village becomes $x-1$ and in the second village becomes $y+1$.The new average incomes are $P^{\prime} = \frac{Px - I}{x-1}$ and $Q^{\prime} = \frac{Qy + I}{y+1}$.If $P^{\prime} = P$,then $Px - I = P(x-1) = Px - P$,which implies $I = P$.If $Q^{\prime} = Q$,then $Qy + I = Q(y+1) = Qy + Q$,which implies $I = Q$.Since $P 
eq Q$,the person cannot have an income $I$ such that both $P^{\prime} = P$ and $Q^{\prime} = Q$ simultaneously.Thus,the condition $P^{\prime} = P$ and $Q^{\prime} = Q$ is impossible.Therefore,option $(C)$ is correct.

Marks:	$2$	$3$	$5$	$7$
Frequency:	$(x+1)^2$	$2x-5$	$x^2-3x$	$x$

The average incomes of the people in two villages are $P$ and $Q$,respectively. Assume that $P \neq Q$. $A$ person moves from the first village to the second village. The new average incomes are $P^{\prime}$ and $Q^{\prime}$,respectively. Which of the following is not possible?

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