Question

The average incomes of the people in two villages are $P$ and $Q$, respectively. Assume that $P\ne Q$. 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?

• A. $P^{\prime }>P$ and $Q^{\prime }>Q$
• B. $P^{\prime }>P$ and $Q^{\prime }<Q$
• C. $P^{\prime }=P$ and $Q^{\prime }=Q$
• D. $P^{\prime }<P$ and $Q^{\prime }<Q$

Answer 1

Answer: (C)

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

Let number of peoples in two villages are $n$ and $m$ respectively
So $nP-P^{\prime }(n-1)=(m+1)Q^{\prime }-mQ$
$n(P-P^{\prime })+P^{\prime }=m(Q^{\prime }-Q)+Q^{\prime }$