My Math Forum Why 5: 3 instead of 3:5?

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

 April 12th, 2018, 10:58 PM #1 Senior Member   Joined: Aug 2014 From: India Posts: 183 Thanks: 1 Why 5: 3 instead of 3:5? In What Ratio must a shopkeeper mix two type of rice worth Rs 50/- per Kg and Rs 58/- per kg so that by selling the mixture of Rs 58.30/- per kg and he may gain 10%? Selling Price of 1 kg of rice of the mixture = 58.30/- Gain = 10% Cost Price of 1 kg of the mixture = 100×58.30/110 = Rs 53/- By the rule of alligation: C.P.M.1 = (Cost Price of First rice) = Rs 50/- C.P.M 2 = (Cost Price of Second Rice) = Rs 58/- M.P = (Mean Price of both material) = Rs 53.00/- So, (C.P.M - M.P) : ( C.P.M.2 - M.P.) = (50 - 53): (58-53) = 5 : 3 Why 5: 3 instead of 3:5? Last edited by Ganesh Ujwal; April 12th, 2018 at 11:43 PM.
 April 13th, 2018, 12:45 PM #2 Global Moderator   Joined: May 2007 Posts: 6,494 Thanks: 577 5|50-53|=3|58-53| to get 53 as the mean price. Another look: (50x5 +58x3)/8=53
April 13th, 2018, 04:57 PM   #3
Senior Member

Joined: Aug 2014
From: India

Posts: 183
Thanks: 1

Quote:
 Originally Posted by mathman 5|50-53|=3|58-53| to get 53 as the mean price. Another look: (50x5 +58x3)/8=53
Still confusing, feel free to ignore my posts next time onwards.

Last edited by skipjack; April 14th, 2018 at 02:41 AM.

 April 14th, 2018, 02:50 AM #4 Global Moderator   Joined: Dec 2006 Posts: 18,838 Thanks: 1564 The ratio (50 - 53) : (58 - 53) simplifies to -3 : 5, so 5(50 - 53) = -3(58 - 53), which implies 5 × 50 + 3 × 58 = 53(5 + 3). Hence the ratio the question asks for is 5 : 3, because (5 × 50 + 3 × 5/(5 + 3) = 53.

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