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Question 211426: Respected sir,
plz help me to slove this % problem.
1] At car delarship X,the total profil from sales increased by 10% over the previous year while the number of cars sold decreased by 10% over the previous year.Approximately what was the average percent increase in profit per car over the previous year?
waiting for yur reply.
Thanks.
Regards
Binita.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Your problem is:
1] At car delarship X,the total profit from sales increased by 10% over the previous year while the number of cars sold decreased by 10% over the previous year.
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Approximately what was the average percent increase in profit per car over the previous year?
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let P = total profit made the previous year.
let C = number of cars sold the previous year.
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Average Profit = Total Profit divided by number of cars sold.
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let A = average profit per car made the previous year.
Formula for calculating average profit per car from the previous year becomes:
A = P/C
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This year the total profit increased by 10% over the previous year.
This makes the total profit this year equal to P + .1*P = 1.1 * P
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This year the number of cars sold decreased by 10% over the previous year.
This makes the total number of cars sold this year equal to C - .1*C which equals .9 * C
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let B = average profit per car made this year.
Formula for calculating average profit per car this year becomes:
B = 1.1 * P / .9 * C
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This is the same as:
B = (1.1/.9) * (P/C)
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1.1/.9 = 1.22222222...
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This means that the average profit this year per car increased 22.222222... % over the average profit per car from the previous year.
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This is how that works.
A = average profit per car last year = P/C
B = average profit per car this year = (1.1*P)/(.9*C)
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(1.1P/.9C)/(P/C) is the same as:
(1.1P/.9C)*(C/P)
P/C cancels out C/P so you are left with 1.1/.9.
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The result is that B/A = 1.1/.9 = 1.22222222... which is the same as an increase of 22.22222... %
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B/A = 1.1/.9 becomes:
B = A*1.1/.9 when you solve for B by multiplying both sides of this equation by A.
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A*1.1/.9 becomes A*1.22222.... when you divide 1.1 by .9.
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A * 1.22222.... is the same as A + .22222... * A
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.22222... * A is the same as 22.22222% * A when you multiply .222 * 100% to turn it into a percent rather than a ratio.
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let me put this into numbers so you can see it better.
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let C = 1,000
let P = 5,000,000
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A = average profit per car = P/C = 5,000,000/1,000 = 5,000 dollars profit per car.
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This year the total profit went up 10% over last year.
P + 10% * P = 1.1 * P = 1.1 * 5,000,000 = 5,500,000
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this year the total number of cars sold went down 10% over last year.
C - 10% * C = .9 * C = .9 * 1,000 = 900
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B = average profit per car this year = 1.1*P/.9*C = 5,500,000/900 = 6111.11111... per car.
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6111.11111... / 5000 = 1.222222222...
This means that average profit per car this year increased by 22.22...% over last year.
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Rounding this to the nearest hundredth of a percent makes the answer equal to:
Average increase in profit per car this year equals 22.22%
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