Question

The difference between the cost price and sale price of an article is \[{\rm{Rs}}240\]. If the profit is \[20\% \], the selling price is:
A.\[{\rm{Rs}}1440\]
B.\[{\rm{Rs}}1400\]
C.\[{\rm{Rs}}1600\]
D.None of these

Answer 1

Hint: Here, we will use the fact that the profit is the difference between the selling price and the cost price when the selling price is greater. We will substitute the given difference and the profit percentage in the formula of profit percentage to find the cost price. Then we will add the cost price to the given difference to find the selling price.

Formula Used:
Profit percentage \[ = \dfrac{{SP - CP}}{{CP}} \times 100\], \[CP\] is the cost price and \[SP\] is the selling price.

Complete step-by-step answer:
Let the cost price of an article be \[CP\]
Let the selling price be \[SP\]
According to the question,
The difference between the cost price and sale price of an article is \[{\rm{Rs}}240\]
Hence, writing this mathematically, we get,
\[CP - SP = {\rm{Rs}}240\]
But, in this question, we are given that there is a profit on this article.
Hence, the Cost price cannot be greater than the selling price.
Thus, we will write the difference between the two as:
\[SP - CP = {\rm{Rs}}240\]
Now, the given profit percentage is \[20\% \]
This means that the profit on the cost price in percentage terms is \[20\% \].
Hence, this can also be written as:
Profit percentage \[ = \dfrac{{{\rm{Profit}}}}{{CP}} \times 100\]
But, we know that Profit is the difference between Selling Price and the Cost Price.
Hence, this can also be written as:
Profit percentage \[ = \dfrac{{SP - CP}}{{CP}} \times 100\]
Now, substituting the known values from above, we get,
\[20 = \dfrac{{240}}{{CP}} \times 100\]
\[ \Rightarrow CP = \dfrac{{240{\kern 1pt} \times 100}}{{20}} = 12 \times 100\]
Hence, we get,
\[ \Rightarrow CP = {\rm{Rs}}1200\]
Hence, substituting this in \[SP - CP = {\rm{Rs}}240\], we get,
\[SP - {\rm{Rs}}1200 = {\rm{Rs}}240\]
\[ \Rightarrow SP = {\rm{Rs}}1440\]
Hence, the required selling price of the given article is \[{\rm{Rs}}1440\]
Therefore, option A is the correct answer.

Note: For solving this question, it is really important to know the difference between Cost Price and Selling Price. We know that Cost Price is the amount at which the retailer/seller has bought the product. Selling Price is the amount at which the buyer/customer is willing to purchase that product. If the C.P. is greater than the S.P then it is a loss for the seller but if the S.P is greater than the CP then it is a profit. Therefore, if we add the amount of profit earned to the Cost Price then, we get the Selling Price.