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kevincan
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This is my attempt. Though it took a bit longer than 2 minutes to solve this.

Total number of people in village yesterday = Y
Total number of people in village today = T

Yesterday
Residents = (1/10)Y
Non-Residents = (9/10)Y

Today
Residents = (3/5)T
Non-Residents = (2/5)T

Yesterdays Residents + 390 = Today's residents
(1/10)Y + 390 = (3/5)T (1)

Yesterdays Non Res - Yest Non Res (5/6) = Today's Non Res
Yest Non Res (1/6) = Today's Non Res
(9/10)*(1/6)Y = (2/5)T
=> Y = (8/3)T

Substitute in (1)
(1/10)(8/3)T + 390 = (3/5)T
=> T= 1170

Therefore, answer is (D) 1170
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..................residents ..... non residents
Yesterday.........x ..................9x
Today ............x + 390...........9x/6= 3x/2

We need to find 5x/2 + 390


(x + 390)/(3x/2) = 3/2

x+ 390 = 9x/4

5x/4 = 390
5x/2 = 780
5x/2 + 390 = 780+ 390 =1,170
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He multiplied by six so that today’s number is clean
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How are you deciding that you should be taking the yesterday's R to NR ratio as 6x:54x?

I understand it is same as 1:10 that is described in the question and your numbers make the calculation easier, but what is your method of arriving at 6, 54 as coefficients and not any other number?
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