Question

A dealer purchases $15$ articles for $25$and sells $12$articles for $30$. Find the profit percentage.
A.$50\% $
B.$40\% $
C.$20\% $
D.$10\% $

Answer 1

Hint: Here, in the question it is already given that the cost price of 15 articles is 25 and the selling price of 12 articles is 30 from which we could determine the cost price and selling price of the single article by unitary method. As we now, the cost price and the selling price of an article then, we can use the formula for the profit percent to determine the result.


Complete step by step solution:
A dealer purchases $15$ articles at Rs $25$ and sells $12$ articles at Rs $30$.
According to question:
CP of 15 articles is Rs. 25
By the unitary method we get,
CP of an article = $\dfrac{{25}}{{15}} = \dfrac{5}{3} = 1.67 - - - - (i)$
Then dealers sell 12 articles at Rs $30$
Again, by the unitary method we get,
SP of an article = \[\dfrac{{30}}{{12}} = \dfrac{5}{2} = 2.5 - - - - (ii)\]
From eq (1) and (2), it is clear that
SP > CP
It means the dealer got a profit in the whole transaction, and according to the question, we have to find a profit percentage.
Now substituting $SP = 2.5$ and $CP = 1.67$ in the formula of ${\text{Profit% = }}\dfrac{{SP - CP}}{{CP}} \times 100$ to determine the profit percentage as:
\[
  {\text{Profit% = }}\dfrac{{SP - CP}}{{CP}} \times 100 \\
   = \dfrac{{2.5 - 1.67}}{{1.67}} \times 100 \\
   = \dfrac{{0.83}}{{1.67}} \times 100 \\
   = 50\% \\
 \]
Hence, the profit percentage is 50%.
Option A is the correct option.

Additional Information: When a product is purchased in the view of selling it to the consumer in order to do business then, the price in which the product is bought by the seller is known as the cost price of the product and the price in which the seller sells the product to the consumer is known as selling of the product for the seller. If the selling price of the product is greater than the cost price of the product, then the difference in the prices can be termed as the profit or the gain on the product while at the same time if the selling price is less than the cost price of the product, then the difference in the price is known as the loss on the product. Profit percent or, loss percent of a product is always calculated on the cost price of the product.


Note: In these types of questions where profit % and loss % have to be solved first, we should know about SP and CP and also how we come to know when its profit or loss.Also,profit percentage can be calculated only when S.P>C.P