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August 1st, 2019, 06:06 PM   #1
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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?
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August 1st, 2019, 07:12 PM   #2
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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.
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August 1st, 2019, 10:55 PM   #3
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Quote:
Originally Posted by Maschke View Post
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?
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August 2nd, 2019, 08:11 AM   #4
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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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