
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
 LinkBack  Thread Tools  Display Modes 
August 1st, 2019, 06:06 PM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 458 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: 2,355 Thanks: 737 
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. [8] 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 
Senior Member Joined: Aug 2014 From: India Posts: 458 Thanks: 1  
August 2nd, 2019, 08:11 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,921 Thanks: 2203 
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 nonzero, 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  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Help UnFry My Brain  Horse Probability  billnc  Probability and Statistics  2  June 5th, 2017 04:28 PM 
About horse racing bet  momo  Advanced Statistics  12  December 8th, 2015 02:45 AM 
angles on a saw horse  mickthetree  Geometry  2  July 12th, 2014 10:01 AM 
the horse  Haley  New Users  6  November 8th, 2012 05:55 AM 
Horse Combinations  M. Einstein  Math Events  0  July 26th, 2009 09:14 AM 