Question

A shopkeeper offers Buy 1 Get 1 Free offer on t-shirt marked at Rs. \[2,400\]. If after a sale, the shopkeeper earns a profit of \[33.33\% \]. Then what is the actual price of the t-shirt?​

Answer 1

Hint: Here in this question, we have to find the cost price of a single t-shirt.Given the selling price of 2 t-shirts and the profit percentage the formula of cost price (C. P) is \[C.P = \dfrac{{\left( {S.P \times 100} \right)}}{{100 + profit\,percentage}}\], where S.P is the selling price of the one t-shirt this can be find by using a selling price of two t-shirts. On substituting in formula and by simplification we get the required solution.

Complete step by step answer:
Consider the given question: a shopkeeper sold two t-shirts at Rs. 2,400 on offering Buy 1 Get 1 free and He earns a profit of percentage \[33.33\% \]. We have to find the actual price or cost price of the one t-shirt? Cost price is also known as C.P. cost price is the original price of an item. The cost is the total outlay required to produce a product or carry out a service.

Formula to calculate cost price if selling price and profit percentage are given:
\[C.P = \dfrac{{\left( {S.P \times 100} \right)}}{{100 + \text{profit percentage}}}\]-----(1)
Where S.P is the selling price of one t-shirt.
One t- shirt selling price can be calculated as:
\[\dfrac{{2400}}{2}\]
\[ \Rightarrow \,\,\,1200\] Rs.
Let us calculate the cost price of t-shirt:
\[ \Rightarrow \,\,\,C.P = \dfrac{{\left( {1200 \times 100} \right)}}{{100 + 33.33}}\]
\[ \Rightarrow \,\,\,C.P = \dfrac{{120,000}}{{133.33}}\]
\[ \Rightarrow \,\,\,C.P = 900.022\]
On rounding-off numbers, we get
\[ \therefore \,\,\,C.P = 900\] Rs

Therefore, actual price or Cost Price Per Shirt is Rs. 900.

Note: Cost price is the initial amount paid for a product. To find a Cost price we have two formulas depending upon profit or loss percentage of a product. Formula to calculate cost price if selling price and profit percentage are given:
\[C.P = \dfrac{{\left( {S.P \times 100} \right)}}{{100 + \text{profit percentage}}}\]
Formula to calculate cost price if selling price and loss percentage are given:
\[C.P = \dfrac{{\left( {S.P \times 100} \right)}}{{100 +\text{loss percentage}}}\].