SOLUTION: The average of two four digit positive integers is found by placing a demimal point between the two numbers. Find the sum of the two four digit numbers.

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Question 65110: The average of two four digit positive integers is found by placing a demimal point between the two numbers. Find the sum of the two four digit numbers.
Answer by venugopalramana(3286) About Me  (Show Source):
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The average of two four digit positive integers is found by placing a demimal point between the two numbers. Find the sum of the two four digit numbers.
LET THE 2 NUMBERS BE
I NUMBER IS....ABCD..ITS VALUE IS = D+ 10C+100B+1000A =M SAY
II NUMBER IS ..PQRS ...ITS VALUE IS = S+10R+100Q+1000P = N SAY
SUM OF 2 NUMBERS = (D+S)+10(C+R)+100(B+Q)+1000(A+P)=M+N
THEIR AVERAGE AS GIVEN = ABCD.PQRS...ITS VALUE IS
= D+ 10C+100B+1000A+P/10 + Q/100 + R/1000 + S/10000 = M+N/10000
= (M+N)/2
HENCE
2M+2N/10000-M-N=0
M-N+N/5000=0
M = N[1-1/5000]=4999N/5000
SINCE M IS ANINTEGER
N SHOULD BE A MULTIPLE OF 5000 = 5000*X
SINCE M & N ARE 4 DIGIT NUMBERS ..THE ONLY POSSIBILITY IS X=1.
HENCE THE 2 NUMBERS ARE
5000 AND 4999 THEIR AVERAGE IS 4999.5000 WHICH IS OK