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 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 August 1st, 2019, 06:06 PM #1 Senior Member   Joined: Aug 2014 From: India Posts: 476 Thanks: 1 what is the C.P of the horse? A horse and a carriage together cost Rs 8000. If by selling the horse at a profit 10% and the carriage at a loss of 10% a total profit of 2.5% is made, then what is the C.P of the horse? Sol: By alligation method: 10----------(-10) ------2.5---------- 12.5 - 7.5 = 5:3 After this, how to proceed? August 1st, 2019, 07:12 PM #2 Senior Member   Joined: Aug 2012 Posts: 2,409 Thanks: 753 I don't know what a C.P. is and I couldn't figure out your method. Here's what I did. Let H be the horse and C the cart. Then (1) H + C = 8000. (2) Total profit is 2.5% of 8000 = 200. (3) So total sale price is 8200. (4) The total sale price is 110% of H plus 90% of C. So ... (5) (11/10)H + (9/10)C = 8200. (6) 11H + 9C = 82,000. (7) From (1), 11H + 11C = 88,000.  Subtracting (6) from (7), 2C = 6000 and C = 3000. (9) Then H = 5000. Plugging the numbers back in to make sure this is right, we have: 110% of 5000 + 90% of 3000 = 5500 + 2700 = 8200. Can you explain how your alligation (allocation?) method works? What does 12.5 - 7.5 = 5:3 mean? If you knew the correct ratio was 5:3 you'd be done but how does that come out of 12.5 - 7.5? Last edited by Maschke; August 1st, 2019 at 07:34 PM. August 1st, 2019, 10:55 PM   #3
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Quote:
 Originally Posted by Maschke What does 12.5 - 7.5 = 5:3 mean? If you knew the correct ratio was 5:3 you'd be done but how does that come out of 12.5 - 7.5?
12.5 : 7.5 = 5:3 (It is the ratio symbol not minus "-" symbol between 12.5 & 7.5)
From here, how to proceed? August 2nd, 2019, 08:11 AM #4 Global Moderator   Joined: Dec 2006 Posts: 21,028 Thanks: 2259 To get the desired 5:3 ratio, first add 5 and 3 to get 8, then the horse cost 5/8 of Rs 8000 and the carriage cost 3/8 of Rs 8000. Algebraically, given three fractions, p, l and t, we want to find m and n, where m + n is known, n is non-zero, and pm - ln = t(m + n). That equation implies m/n = (l + t)/(p - t). This approach was posted originally. One could alternatively remember the solution m = ((l + t)/(p + l))(m + n). Tags horse Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post billnc Probability and Statistics 2 June 5th, 2017 04:28 PM momo Advanced Statistics 12 December 8th, 2015 02:45 AM mickthetree Geometry 2 July 12th, 2014 10:01 AM Haley New Users 6 November 8th, 2012 05:55 AM M. Einstein Math Events 0 July 26th, 2009 09:14 AM

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