
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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April 16th, 2018, 01:07 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 310 Thanks: 1  Kiran bought some goods for 720 rs....
Kiran bought some goods for 720 rs. He sold one fourth 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%? [Ans : 23%] I tried: CP = 720 / $\dfrac {1}{4}$ x = 15% $\dfrac {3}{4}$ X = y % Total profit = 21% How can I continue from here? Last edited by skipjack; April 16th, 2018 at 04:46 AM. 
April 16th, 2018, 03:45 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
I am glad to see that you have tried to do this yourself first, but I am not sure I follow your logic. Rather than just writing everything out is one large arithmetic operation, it would be better to do one step at a time and explain why you are doing it. Here is what I would do: "Kiran bought some goods for 720 rs. He sold one forth of the goods at a profit of 15%." Okay, 1/4 of 720 rs is 720/4= 180. 15% of that is 27 Rs. "At what profit percentage should he sell the remaining goods to gain an overall profit of 21%?" 21% of the original 720 rs would be 151.2 Rs. Since Kiran has already made 27Rs profit, he must make 151.2 27= 124.2 Rs profit on the remaining 720 180= 540 Rs of goods. 124.2 on 540 is 124.2/540= 23% profit on the remaining goods. Notice that this is a 'weighted average'. 1/4 of the goods at 15% and 3/4 at 21% is an average of (1/4)(15)+ (3/4)(23)= 21. We could have done this by solving (1/4)(15)+ (3/4)x= 21 but the way I showed first follows more directly from the information given. 
April 16th, 2018, 03:54 AM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,103 Thanks: 907 
p = profit percentage required: 720(1.21) = 180(1.15) + 540(1+p) Solve for p: you should get .23 
April 16th, 2018, 05:05 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,508 Thanks: 1741  
April 16th, 2018, 07:36 AM  #5 
Senior Member Joined: Aug 2014 From: India Posts: 310 Thanks: 1  

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