Question

Ankit bought a pair of shoes at a discount \[30\% \]. If he paid \[{\text{Rs}}.1250\] then find the marked price?

Answer 1

Hint: Here we will be using the formula for calculating the marked price when the selling price is given which is as below:
\[ \Rightarrow {\text{S}}{\text{.P}} = \left( {100 - {\text{discount}}} \right)\% \times {\text{M}}{\text{.P}}\]
Where S.P is the selling price of the product, the discount percentage is the discount percent given on that product and M.P denotes the marked price.

Complete step-by-step solution:
Step 1: We will assume that the Marked price of the product is
\[x\]. As per the given information in the question, the selling price of the product is \[{\text{Rs}}.1250\] at a discount percentage
\[30\% \]. By using the formula of marked price w.r.t selling price, we get:
\[ \Rightarrow {\text{S}}{\text{.P}} = \left( {100 - {\text{discount}}} \right)\% \times x\]
Step 2: By substituting the values of selling price and discount percentage in the above expression
\[{\text{S}}{\text{.P}} = \left( {100 - {\text{discount}}} \right)\% \times x\], we get:
\[ \Rightarrow 1250 = \left( {100 - 30} \right)\% \times x\]
By simplifying the brackets and subtracting the terms in the RHS side of the above expression, we get:
\[ \Rightarrow 1250 = 70\% \times x\]
By replacing \[70\% = \dfrac{{70}}{{100}}\], in the above expression, we get:
\[ \Rightarrow 1250 = \dfrac{{70}}{{100}} \times x\]
Bringing \[\dfrac{{70}}{{100}}\] into the LHS side of the above expression, we get:
\[ \Rightarrow \dfrac{{1250 \times 100}}{{70}} = x\]
By dividing the LHS side of the above expression, we get:
\[ \Rightarrow x = {\text{Rs}}.1785.71\]

The marked price of the product is \[{\text{Rs}}.1785.71\].

Note: Students should remember the difference between the Marked price and the selling price. Marked price is one which is mentioned on the label of the product and selling price is that price at which any particular product is sold to the customer.
You should remember some basics formula for calculating the terms selling price/cost price/marked price, as given below:
The selling price of the product when the cost price and profit percentage is given:
\[ \Rightarrow {\text{S}}{\text{.P}} = \dfrac{{\left( {100 + {\text{profit}}} \right)\% }}{{100}} \times {\text{C}}{\text{.P}}\]
The selling price of the product when the cost price and loss percentage is given:
\[ \Rightarrow {\text{S}}{\text{.P}} = \dfrac{{\left( {100 - {\text{loss}}} \right)\% }}{{100}} \times {\text{C}}{\text{.P}}\]
The cost price of the product when selling price and profit percentage is given:
\[ \Rightarrow {\text{C}}{\text{.P}} = \dfrac{{100}}{{\left( {100 + {\text{profit}}} \right)\% }} \times {\text{S}}{\text{.P}}\]
The cost price of the product when selling price and loss percentage is given:
\[ \Rightarrow {\text{C}}{\text{.P}} = \dfrac{{100}}{{\left( {100 - {\text{loss}}} \right)\% }} \times {\text{S}}{\text{.P}}\]