Question

A shopkeeper buys 80 articles for Rs. 2400 and sells them for a profit of $16%$. Find the selling price of one article.

Answer 1

Hint: Find the cost of 1 article. By using the profit percentage formula, find the profit for 1 article. Now, we know profit and CP, thus find SP by directly substituting these values in the formula. Find SP of 1 article.

Complete step-by-step answer:
It is said that the shopkeeper buys 80 articles. The articles cost Rs. 2400.
i.e., Cost price of 1 article \[=\ \dfrac{2400}{80}\ =\ \text{Rs}\text{. 30}\]
Hence, we got the cost price of 1 article as Rs. 30.
We are also given the profit percentage of the article as $16%$.
We know the formula for profit percentage as
\[\text{profit percentage =}\ \dfrac{\text{Profit}}{\text{CP}}\times 100\]
We know profit percentage $=16%$ and CP $\text{Rs}\text{. }30$. Thus, find the profit made by one article in rupees.
\[\text{profit percentage =}\ \dfrac{\text{Profit}}{\text{CP}}\times 100\]
\[\text{16 =}\ \dfrac{\text{Profit}}{30}\times 100\]
\[\text{Profit =}\ \dfrac{16\times 30}{100}\ =\ \dfrac{480}{100}\ =\ \text{Rs}\text{. 4}\text{.8}\]
Hence the shopkeeper got a profit of Rs. 4.8 for one article.
We know \[\text{Profit}\ \text{=}\ \text{Selling price}-\text{Cost price}\]
\[\text{Profit}\ \text{=}\ \text{SP}-\text{CP}\]
\[\text{SP}\ \text{=}\ \text{4}\text{.8+30}\ \text{=}\ \text{34}\text{.8}\]
Hence, we got the selling price of the article as Rs. 34.8.

Note: If we are asked to find the selling price of all the 80 articles then multiply 80 with the selling price of one article.
i.e. selling price of 80 articles $=\ 80\times 34.8\ =\ \text{Rs}\text{. 2784}$
Hence, his selling price of all 80 articles is Rs. 2784.