June 15th, 2018, 09:15 PM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 361 Thanks: 1  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 (720180)*x=871.2207 > 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 (720180)*x=871.2207 ? 
June 15th, 2018, 09:32 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs 
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: $\displaystyle 115+300(1+x)=484$ $\displaystyle 300(1+x)=369$ $\displaystyle 1+x=\frac{123}{100}$ $\displaystyle x=\frac{23}{100}=23\%$ Last edited by MarkFL; June 15th, 2018 at 09:42 PM. 
June 15th, 2018, 09:35 PM  #3 
Senior Member Joined: Aug 2014 From: India Posts: 361 Thanks: 1  
June 15th, 2018, 09:41 PM  #4  
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Quote:
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.  
June 15th, 2018, 09:50 PM  #5 
Senior Member Joined: Aug 2014 From: India Posts: 361 Thanks: 1 
Why 1+X instead of Just X?

June 15th, 2018, 10:02 PM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs 
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. 
June 15th, 2018, 10:03 PM  #7 
Newbie Joined: Jun 2018 From: USA Posts: 2 Thanks: 0 
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 (871.2207=664.2) by selling the other 3/4 part. Initial price of 3/4 part is (720180). So if x is the multiplying factor including the increase percentage(for 15% increase, the factor is 1+0.15=1.15) (720180)*x=871.2207 x=1.23 so he should sell the 3/4 part at 23% profit. 
June 16th, 2018, 02:13 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 20,746 Thanks: 2133 
x = (871.2  207)/(720  180) = 664.2/540 = 110.7/90 = 1.23

June 16th, 2018, 04:20 AM  #9 
Senior Member Joined: Aug 2014 From: India Posts: 361 Thanks: 1  
June 16th, 2018, 08:54 AM  #10 
Global Moderator Joined: Dec 2006 Posts: 20,746 Thanks: 2133 
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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