
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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April 12th, 2018, 10:58 PM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 294 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): (5853) = 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: 6,540 Thanks: 591 
55053=35853 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: 294 Thanks: 1  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: 19,174 Thanks: 1644 
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. 