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Question

The average incomes of the people in two villages are P and Q, respectively. Assume that P≠Q. A person moves from the first village to the second village. The new average incomes are P′ and Q′, respectively. Which of the following is not possible ?

A
P>P and Q>Q
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B
P>P and Q<Q
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C
P=P and Q=Q
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D
P<P and Q<Q
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Solution

The correct option is C P=P and Q=Q
Average incomes of the people in first villages P=x1+x2+....+xnn and average incomes of the people in second villages Q=y1+y2+....+ymm
x1+x2+....+xn=nP & y1+y2+....+ym=mQ
Now if a person moves from first village to second village then
x1+x2+....+xn1n1=PnPxn=(n1)P
P=nn1Pxnn1
and
y1+y2+....+ym+xnm+1=QmQ+xn=(m+1)Q
Now if P=P(1nn1)P=xnn1P=xn
Also if Q=QQ=xn
Hence, P=Q which is not possible as PQ

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