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A person purchased some articles he sold 1/3 at profit of 14%, 3/5 articles at profit of 17(1/2) % and rest at profit of 20%. Find his total profit %.
- a)10%
- b)18.5%
- c)16.5%
- d)16%
Correct answer is option 'C'. Can you explain this answer?
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A person purchased some articles he sold1/3at profit of 14%,3/5article...
= 16.5%
Most Upvoted Answer
A person purchased some articles he sold1/3at profit of 14%,3/5article...
To find the total profit percentage, we need to calculate the profit earned on each group of articles separately and then find the average of these profits.
Let's assume that the person purchased a total of 100 articles.
Profit on the first group of articles:
The person sold 1/3 of the articles at a profit of 14%.
So, the number of articles in this group = 1/3 * 100 = 33.33 (approximated to 33).
The profit earned on this group of articles = 33 * 14/100 = 4.62 (approximated to 4.6).
Profit on the second group of articles:
The person sold 3/5 of the articles at a profit of 17(1/2)%.
So, the number of articles in this group = 3/5 * 100 = 60.
The profit earned on this group of articles = 60 * 17.5/100 = 10.5.
Profit on the third group of articles:
The remaining articles are sold at a profit of 20%.
So, the number of articles in this group = Total articles - (Articles in the first group + Articles in the second group) = 100 - (33 + 60) = 7.
The profit earned on this group of articles = 7 * 20/100 = 1.4.
Total profit earned = Profit on the first group + Profit on the second group + Profit on the third group
= 4.6 + 10.5 + 1.4 = 16.5.
Now, let's calculate the total cost price of the articles:
The cost price of the first group of articles = 33 (as assumed)
The cost price of the second group of articles = 60 (as assumed)
The cost price of the third group of articles = 7 (as assumed)
Total cost price = Cost price of the first group + Cost price of the second group + Cost price of the third group
= 33 + 60 + 7 = 100.
Finally, the total profit percentage = (Total profit earned / Total cost price) * 100
= (16.5 / 100) * 100 = 16.5%.
Therefore, the correct answer is option 'C', 16.5%.
Let's assume that the person purchased a total of 100 articles.
Profit on the first group of articles:
The person sold 1/3 of the articles at a profit of 14%.
So, the number of articles in this group = 1/3 * 100 = 33.33 (approximated to 33).
The profit earned on this group of articles = 33 * 14/100 = 4.62 (approximated to 4.6).
Profit on the second group of articles:
The person sold 3/5 of the articles at a profit of 17(1/2)%.
So, the number of articles in this group = 3/5 * 100 = 60.
The profit earned on this group of articles = 60 * 17.5/100 = 10.5.
Profit on the third group of articles:
The remaining articles are sold at a profit of 20%.
So, the number of articles in this group = Total articles - (Articles in the first group + Articles in the second group) = 100 - (33 + 60) = 7.
The profit earned on this group of articles = 7 * 20/100 = 1.4.
Total profit earned = Profit on the first group + Profit on the second group + Profit on the third group
= 4.6 + 10.5 + 1.4 = 16.5.
Now, let's calculate the total cost price of the articles:
The cost price of the first group of articles = 33 (as assumed)
The cost price of the second group of articles = 60 (as assumed)
The cost price of the third group of articles = 7 (as assumed)
Total cost price = Cost price of the first group + Cost price of the second group + Cost price of the third group
= 33 + 60 + 7 = 100.
Finally, the total profit percentage = (Total profit earned / Total cost price) * 100
= (16.5 / 100) * 100 = 16.5%.
Therefore, the correct answer is option 'C', 16.5%.
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