Bunuel wrote:
If John purchased goods for $1050, and sold 1/3rd of these goods at a loss of 12%, then at what gain percent should remainder goods be sold to gain 18% on the whole transaction?
A. 31%
B. 33%
C. 43%
D. 67%
E. 77%
Understand that the question is asking about
gain PERCENT.
To determine a percentage value, we can, actually ignore the $1050 information and solve it using any suitable value as well, say $300 instead (this makes the calculations way easier). Let us see:
Let the total purchase price be $300
Thus, purchase price of \(1/3rd\) of these = \(1/3 * $300 = $100\)
Loss incurred = 12%
=> Selling price of these \(1/3rd\) goods = $88
Required gain overall = 18%
=> Required TOTAL selling price = \(118% of $300 = $354\)
Thus, selling price of the remaining \((1 - 1/3 =) 2/3rd\) goods = \($(354 - 88) = $266\)
Purchase price of this stock of \(2/3rd\) goods = \(2/3 * $300 = $200\)
=> Required percent profit = \([(266 - 200)/200] * 100 = 33%\)
Answer BAlternate approach: Now that we are clear that the actual price of $1050 is NOT necessary, let us try to solve this using a method where we do NOT need to assume any values at all!
Let us look at the data available:
You have some goods (Note: the cost price per unit is the SAME since the goods are identical)
You sell \(1/3rd\) making 12% loss =>
Net contribution = \(1/3 * (-12) = -4\)
You need to make overall 18% profit =>
Net overall = \(+18\)
Thus, contribution required from the remaining \(2/3rd\) = \(18 - (-4) = 22\)
(Note: If we add 22 with '-4', only then we get 18)
Thus, from the \(2/3rd\) stock, you intend to get a contribution of 22
=> Required profit % of this remaining \(2/3rd\) stock = \(22/(2/3) = 22 * 3/2\) =
33%[Relate to the first step: 2/3rd making 33% gain => Net contribution = 2/3 * (+33) = +22]
Voila! A simple 30 second approach to solve this question
_________________
Sujoy Kumar Datta
Director - CUBIX Educational Institute Pvt. Ltd. (https://www.cubixprep.com)
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IIT Kharagpur, TU Dresden Germany
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