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June 15th, 2018, 09:15 PM   #1
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How is this step obtained

Kiran bought some goods for 720/- He sold one forth of the goods at a profit of 15% At what profit percentage should he sell the remaining goods to gain an overall profit of 21%?

Solution: The amount of money Kiran wants to end up with is 720 * 1.21 = 871.2

He already sold one forth of it for which he made a profit of 15%.

720/4=180 and 180*1.15=207

So we need to find x so that (720-180)*x=871.2-207

--> 540x=664.2 --> x≈1.23 so he needs to sell the remaining goods at 23% profit.

How is this step obtained: So we need to find x so that (720-180)*x=871.2-207 ?
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June 15th, 2018, 09:32 PM   #2
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I think I'd use a weighted average here:

$\displaystyle \frac{1}{4}\cdot1.15+\frac{3}{4}(1+x)=1.21$

Multiply through by 400:

$\displaystyle 115+300(1+x)=484$

$\displaystyle 300(1+x)=369$

$\displaystyle 1+x=\frac{123}{100}$

$\displaystyle x=\frac{23}{100}=23\%$
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Last edited by MarkFL; June 15th, 2018 at 09:42 PM.
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June 15th, 2018, 09:35 PM   #3
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Quote:
Originally Posted by MarkFL View Post
I think I'd use a weighted average here.

Multiply through by 400:
In what cases should I use "weighted average"?

why did you multiple with 400?
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June 15th, 2018, 09:41 PM   #4
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Quote:
Originally Posted by Ganesh Ujwal View Post
In what cases should I use "weighted average"?

why did you multiple with 400?
A weighted average is "an average resulting from the multiplication of each component by a factor reflecting its importance."

Here we had 1/4 of an amount increased by 15% and the remaining 3/4 increased by an unknown percentage, and we require that the overall increase be 21%. So, this is a good time to apply a weighted average.

I multiplied by 400 to get rid of the denominators in the fractions and to make the decimal values integers. The denominators are 4and the decimal values have 2 places, so a factor of 400 will do both at the same time.
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June 15th, 2018, 09:50 PM   #5
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Why 1+X instead of Just X?
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June 15th, 2018, 10:02 PM   #6
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I wanted just the percentage increase. If you are going to increase an amount by 25%, you would multiply that amount by:

1 + .25 = 1.25

Suppose we wish to increase the quantity r by 25%, we would want to take r and add 25% or r:

r + .25r = r(1 + .25) = 1.25r

In the equation I posted, I wanted x to represent just the increase.
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June 15th, 2018, 10:03 PM   #7
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Kiran should get 871.2 to get final profit percent of 21%
by selling 1/4 at 15% profit, he got 207.
So he should get (871.2-207=664.2) by selling the other 3/4 part.
Initial price of 3/4 part is (720-180).
So if x is the multiplying factor including the increase percentage(for 15% increase, the factor is 1+0.15=1.15)
(720-180)*x=871.2-207
x=1.23
so he should sell the 3/4 part at 23% profit.
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June 16th, 2018, 02:13 AM   #8
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x = (871.2 - 207)/(720 - 180) = 664.2/540 = 110.7/90 = 1.23
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June 16th, 2018, 04:20 AM   #9
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Quote:
Originally Posted by skipjack View Post
x = (871.2 - 207)/(720 - 180)
What formula have you used?
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June 16th, 2018, 08:54 AM   #10
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I used profit on 3/4 of the goods = overall profit - profit on 1/4 of the goods, then I evaluated the numerator and denominator separately and used 540 = 6*90 to allow the division to be done by dividing first by 6 and then by 90.
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