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April 12th, 2018, 10:58 PM   #1
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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.
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April 13th, 2018, 12:45 PM   #2
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5|50-53|=3|58-53| to get 53 as the mean price. Another look:

(50x5 +58x3)/8=53
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April 13th, 2018, 04:57 PM   #3
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Quote:
Originally Posted by mathman View Post
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.
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April 14th, 2018, 02:50 AM   #4
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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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