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June 30th, 2018, 11:15 PM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  How is this big formula obtained?
A man bought 90 watches and marked a tag price 25% of the C.P He started to give 10% discount for the cash payment and 5% discount for others He sold 3/4 of the stock in cash payment. If he earned 2250 as a profit. Find the cost of each watch. Solution: X(5/4)(9/10)(30) + X(5/4)(19/20)(10) = 2250 How is this big formula obtained? 
June 30th, 2018, 11:42 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs 
Are you sure the man didn't buy 40 watches instead of 90?

June 30th, 2018, 11:50 PM  #3 
Senior Member Joined: Sep 2015 From: USA Posts: 2,311 Thanks: 1223  
June 30th, 2018, 11:54 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  
July 1st, 2018, 12:50 AM  #5 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1 
Oh sorry it is 40 watches

July 1st, 2018, 01:16 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,285 Thanks: 1967  
July 1st, 2018, 09:05 AM  #7  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,958 Thanks: 991 
Your problem reworded: Quote:
5/4 = 1.25 (tag price = C.P. + 25%) 9/10 = .9 = 1  .10 (cash payment price reduced by 10%) 30 = 3/4 * 40 (number sold as cash payment) Do you understand that?  
July 1st, 2018, 09:17 PM  #8 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  
July 1st, 2018, 10:56 PM  #9 
Global Moderator Joined: Dec 2006 Posts: 20,285 Thanks: 1967 
The multiplication by 5/4 to get the tag price is because that is equivalent to adding 25% to the CP. Similarly, the multiplication by 9/10 is because that is equivalent to giving a discount of 10% of the tag price. The multiplication by 30 is to give the total amount received for 30 watches that were sold at a 10% discount. These multiplications could be done in succession, but the result would be the same as the result of doing them all together.

July 2nd, 2018, 11:10 AM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,958 Thanks: 991  You also goofed up on the shown solution; should be: X = cost price of 1 watch (ALWAYS declare your variables!) X(5/4)(9/10)(30) + X(5/4)(19/20)(10)  40X = 2250 Solve: X = 400 May we ask you to be more careful? Thank you. 

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