Question

Find the profit percent or loss percent made, when the SP of the 15 identical articles is equal to the CP of 20 articles.
A. Profit $ = 33\dfrac{1}{3}\% $
B. Profit $ = 23\dfrac{1}{2}\% $
C. Profit $=23\dfrac{1}{3}%$
D. Loss $ = 31\dfrac{1}{8}\% $

Answer 1

Hint: If the selling price of an article is more than its cost price, then it is a case of profit while if the selling price of an article is less than its cost price, then it is a case of loss, this can be calculated by
Profit percent , $P = \dfrac{{SP - CP}}{{CP}} \times 100$ and Loss percent, $L = \dfrac{{CP - SP}}{{CP}} \times 100$

Complete step by step answer:
 The SP of 15 identical articles = CP of 20 articles
Therefore, it is clear that
 SP of 1 article = CP of $\dfrac{{20}}{{15}} = \dfrac{4}{3}$ articles
It can be concluded that if an article is purchased at a Cost Price =100 Rs.
Then the selling price of that article $ = \dfrac{4}{3} \times 100 = \dfrac{{400}}{3}$ Rs.
The value is clearly more than 100 which is the cost price of the article. Therefore, it is a case of profit.
Profit is given by,
$P = \dfrac{{SP - CP}}{{CP}}......(1)$

Substituting the value of $SP = \dfrac{{400}}{3}$ and $CP = 100$ in equation (1)
$
\Rightarrow P = \dfrac{{\dfrac{{400}}{3} - 100}}{{100}} \times 100 \\
\Rightarrow P = \dfrac{{400}}{3} - 100 \\
\Rightarrow P = \dfrac{{400 - 300}}{3} \\
\Rightarrow P = \dfrac{{100}}{3}\% \\
\Rightarrow P = 33\dfrac{1}{3}\% \\
 $
Thus, if the selling price of 15 identical articles are equal to the cost price of 20 articles then there is a profit of $33\dfrac{1}{3}\% $.

Hence, the Correct option is (A).

Note: The definitions of the important terms are with an example in which a shopkeeper purchases certain goods from the market and sells it to the customer.
1. Cost Price (CP): It is the price at which the goods are purchased from the market.
2. Selling Price (SP): It is the price at which the goods are sold to the customers.
3. Profit (P): If the selling price is more than cost price, then the shopkeeper earns a profit.
4. Loss (P): if the selling price is less than the cost price, then the shop keeper experiences a loss.