A trader sold one third of his stocks X at a profit percentage of 10%

Question

A trader sold one third of his stocks X at a profit percentage of 10% and the rest at a profit percentage of 25%. What is his overall profit percentage?

A. 12%
B. 15%
C. 18%
D. 20%
E. 21%

yashwardhan · Answer

Let stocks be x

(1/3x*1.1) +(2/3x*1.25) - he sold 1/3rd of the stocks at a profit of 10% and the remaining 2/3rd of the stocks at a profit of 25%

1.1x/3 + 2.5x/3
3.6x/3
1.2x

Change in percentage = (1.2x-x)/x =0.2x/x = 0.2% or 20%

Hence he sold the stocks at an overall profit of 20%

Answer: D

CrackverbalGMAT · Answer

1/3 is sold at profit of 10% and 2/3 at a profit of 25%

Then overall profit =  \frac{1}{3}  * 10 +  \frac{2}{3}  * 25 =  \frac{10 + 50}{3}  =  \frac{60}{3}  = 20%

Option D
_______________
This is a type of Profit and Loss sum where a part is sold at a profit (or loss) and another part is sold at profit (or loss) and we need to find overall profit (or loss). 
Here profit percentages are taken as positive and loss as negative, and the problem can be solved using a straight line formula as done in the question above.

For eg Tom sells  \frac{1}{5}  of his goods for a loss of 6%. At what % profit should he sell his remaining goods to get an overall profit of 2%.

Take the profit % of remaining goods as x%. Then  \frac{1}{5}  * (-6) +  \frac{4}{5}  * (x) = 2

Solving -6 + 4x = 10
4x = 16
x = 4%

_________________

Arun Kumar

QuantMadeEasy · Answer

Step 1: Understanding the question 
One third of the stock are sold at a profit of 10% and remaining two-third are sold at 25% profit.
Let total number of stock be 3 and CP of each stock be 100.
Therefore, number of stocks sold at 10% profit is 1 and 25% profit are 2.

Step 2: Calculation 
SP of 1-stock sold at 10% profit = 1.25*100 = 110
SP of 2 stocks sold at 25% profit = 2*1.25*100 = 250
Total SP = 110+250 = 360
Total CP = 300

Overall profit = 60

Overall Profit percent is  \frac{profit}{CP}  *100 =  \frac{60}{300}  * 100 = 20%

(D) is correct.

bumpbot · Answer

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A trader sold one third of his stocks X at a profit percentage of 10%

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A trader sold one third of his stocks X at a profit percentage of 10%

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