Question

A man sells two articles for the same price for Rs. 640. He earns 20% profit on the first and 10% profit on the second. Find the overall percent profit.
A. 14.78%
B. 14.08%
C. 14.58%
D. 14.68%

Answer 1

Hint: Let us find the cost price of both articles by using the selling price and profit percentage given and find the total profit in two articles by subtracting the selling price with the cost price of both articles.

Complete Step-by-Step solution:
As we know that the cost price of any article is the price at which the shopkeeper (seller) buys that article means the price at which profit is equal to zero.
And the selling price of the article is the price at which the shopkeeper(seller) sells that article.
And if the cost price is greater than selling price then there is loss to the shopkeeper but the selling price is more than the cost price than there is profit.
Here we are given with the selling price of two articles and that is equal to Rs. 640 for each article.
Now as we know that profit in articles of first type is 20%.
So, the selling price (Rs. 640) will be 20% more than the cost price of the first type of article.
According to the percentage formula A% of B is written as \[\dfrac{A}{{100}} \times B\].
So, 120% of the cost price will be equal to 640.
So, applying the percentage formula.
\[S.P = \dfrac{{120}}{{100}} \times C.P\]
S.P is the selling price of an article of first type and C.P is the cost price of an article of first type.
640 = \[\dfrac{{120}}{{100}} \times C.P\]
Multiplying both sides of the above equation by \[\dfrac{{100}}{{120}}\]. We get,
C.P = \[\dfrac{{1600}}{3}\]= Rs. 533.33
Now we had to find the cost price of the second type of article.
Profit on articles of second type is 10%.
So, 110% of the cost price will be equal to 640.
So, applying the percentage formula.
\[S.P = \dfrac{{110}}{{100}} \times C.P\]
S.P is the selling price of articles of second type and C.P is the cost price of articles of second type.
640 = \[\dfrac{{110}}{{100}} \times C.P\]
Multiplying both sides of the above equation by \[\dfrac{{100}}{{110}}\]. We get,
C.P = \[\dfrac{{6400}}{{11}}\]= Rs. 581.81
Now the total cost price of both the articles will be = Rs. 533.33 + Rs. 581.81 = Rs. 1115.14
And the total selling price of both the articles will be = Rs. 640 + Rs. 640 = Rs. 1280
Now the selling price is more than the cost price. So, men sell the articles for profit.
And profit is equal to Rs. 1280 – Rs. 1115.14 = Rs. 164.86
Now applying the percentage formula to find the total profit percentage.
Profit percentage = \[\dfrac{{164.86}}{{1115.14}} \times 100\] = 14.78 %
So, the correct option will be A.

Note: Whenever we come up with this type of problem then we should take care while finding profit percentage because profit is calculated from cost price not selling price so, we had to apply formula \[\left( {{\text{Profit}}\% = \dfrac{{{\text{profit}}}}{{{\text{cost price}}}} \times 100} \right)\] to find the profit. And if the cost price is more than the selling price then there was loss otherwise there was profit in the sale.