If John purchased goods for $1050, and sold 1/3rd of these goods at a

Solution:
In this question, we are given percentage values and the answer is also asked in percentage. We can solve this question by assuming the cost price of \(\frac{1}{3}\) of the goods to be $100 irrespective of what cost price is given in the question. By doing this we can avoid too many fractions here.
Let the Cost price of \(\frac{1}{3}\) goods = $ 100

• It is sold at 12% loss

o Loss = \(\frac{12}{100}\)*100= $ 12

Overall cost price = 3*cost of \(\frac{1}{3}\) of the goods = 3*100=$300

• Overall profit we want = 18%

o Overall profit = \(\frac{18}{100}\)*300= $54

Cost price of remaining goods = 300-100=$200

• Profit = overall profit + overcoming the loss = 54 + 12 = $66

o Profit % = \(\frac{66}{200}\)*100= 33%

Hence the answer is option B.

Solution:
The shortest and fastest way to solve this problem is by the weighted average method.

• \(\frac{1}{3}\) of the goods are sold at 12% loss.
• Let the profit of remaining \(\frac{2}{3}\) of the goods be x%.

o The ratio of\(\frac{ 1}{3}\) and\(\frac{ 2}{3 }\)= 1: 2

We want the overall profit of 18%
We can form the equation as shown below:

• \(\frac{1*-12\% + 2*x\%}{3}\)=18%

o -12+ 2x = 54
o 2x = 66

o x =33

Hence, the correct answer is Option B.
Note- We solved this question without even using the cost price given in the question, this is because the values are given in percentage terms and the answer is also asked in percentage.

Total cost price = 1050
Cost price of 1/3 = 1050*(1/3) = 350 and

Selling price of 350 at a loss of 12% = 350*(88/100) = 308
Selling price of 1050 at 18% gain = 1050*(118/100) = 1239

Selling price of remaining cost price of 700 = 1239-308 = 931
Gain percentage of the remainder = (SP- CP)/CP = (931-700)*100/700 = (231/700)*100 = 231/7% = 33% (B)

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 B




Alternate 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

We don't need to calculate the units and technically the 1050 is irrelevant.

One unit at loss of 12 is -12 and 2 units lets say at the profit of 33 is 66.

The resultant value is 66-12=54/3units = 18

Thats what we want. Option B.

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