My Math Forum what is the C.P of the horse?

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 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. [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
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Joined: Aug 2014
From: India

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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).

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