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June 25th, 2018, 11:08 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  Why equating CP to SP/1.35?
A tradesman gives 4% discount on the marked price and gives 1 article free for buying every 15 articles and thus gains 35%. The marked price is above the cost price by: Ans is 50% Solution: Let the Marked Price (MP) = 100; Selling Price, SP = 4% discount on MP = 96; He effectively sells 16 for the cost of 15; so the cost of one article is 15/16 SP = 90. This gives his gain of 35%, so (SP  CP)/CP = 0.35; CP = SP/1.35 = 66.66 (MP  CP)/CP = 0.5 I didn't understand how is this equation is written: CP= SP/1.35? (or) Why equating CP to SP/1.35? Last edited by skipjack; June 29th, 2018 at 08:01 AM. 
June 25th, 2018, 02:24 PM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,448 Thanks: 946 
200 * 1.35 = 270 : cost 200 sold at 35% profit 270 / 1.35 = 200 
June 26th, 2018, 02:09 AM  #3 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  
June 26th, 2018, 04:34 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
The "cost price" is CP, the "marked price" is MP, and the final "selling price" is SP. "A tradesman gives 4% discount on the marked price and gives 1 article free for buying every 15 articles and thus gains 35%." Do you understand what is meant by such things as "cost price" and "selling price"? The "cost price" is the amount the tradesman paid for an item that he then sells for the "selling price". The tradesman's profit is the difference between the two prices: profit is SP CP. Equivalently, his selling price is the cost price plus his profit. He gains a 35% profit on the cost price that is, his selling price is the cost price plus 35% of the cost price: SP= CP+ 0.35CP= 1.35 CP. Dividing both sides of SP= 1.35 CP by 1.35, that is the same as CP= SP/1.35. 
June 26th, 2018, 05:50 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,448 Thanks: 946 
Example: selling price = 300 + 12% tax tax = 300 * .12 = 36 so selling price = 300 + 36 = 336 This is a shortcut: selling price = 300 * 1.12 = 336 
June 26th, 2018, 03:14 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 19,865 Thanks: 1833 
Let CP be the cost price of each article and MP be its marked price. The tradesman bought 16 articles for 16CP and sold them for 15MP(1  0.04) in total. As the 35% gain means that the articles were sold for a total of 16CP(1 + 0.35), 15MP(1  0.04) = 16CP(1 + 0.35), and so MP/CP = $\displaystyle \small\frac{16(1 + 0.35)}{15(1  0.04)}$ = 1.50. Hence MP is 50% more than CP. 
June 29th, 2018, 12:09 AM  #7 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  Great logic, but you forget to include discount 4%. Please reply again with proper answer.

June 29th, 2018, 01:00 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 19,865 Thanks: 1833 
The discount wasn't forgotten. It was taken into account in your original post, where you stated "SP = 4% discount on MP = 96".

June 29th, 2018, 01:36 AM  #9 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  
June 29th, 2018, 08:16 AM  #10 
Global Moderator Joined: Dec 2006 Posts: 19,865 Thanks: 1833 
The original question gives neither the MP nor the CP, so SP can't be evaluated, but the stated gain of 35% implies that SP = CP + (35/100)CP = 1.35CP. The question tells you the same SP = MP  (4/100)MP, but this can't be evaluated unless a value is assumed for MP. It isn't necessary to do that in order to answer the question. The question lets you write the SP is terms of the CP or in terms of the MP, which means that you can relate the MP to the CP without knowing or assuming any of the prices. 

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