Question

A shopkeeper allows $20\% $ discount on the advertised prices of his goods and still makes a profit of $12\% $ on his cost price. Calculate the advertised price of an article on which gains Rs. 135.

Answer 1

Hint: In these type of question we need to assume some variable value of the advertised price and follow up the question. As profit percent is always equal to $\dfrac{{{\text{Selling}}\,{\text{Price}} - {\text{Cost}}\,{\text{Price}}}}{{{\text{Cost}}\,{\text{Price}}}} \times 100$ and gain is always equal to difference of selling price and cost price.

Complete step by step answer:
Let, the advertised price be Rs x.
Given, the selling price is $20\% $ less (discount) than the advertised price.
So,
$
  {\text{Selling}}\,{\text{Price}} = x - \dfrac{{20}}{{100}} \times x \\
   = x - \dfrac{x}{5} \\
   = \dfrac{{4x}}{5} \\
 $
Therefore, the selling price of an article is $\dfrac{{4x}}{5}$.
It is also given that the profit percentage gained by the shopkeeper is $12\% $ on the cost price.
As, ${\text{Profit}}\,{\text{Percent}} = \dfrac{{{\text{Selling}}\,{\text{Price}} - {\text{Cost}}\,{\text{Price}}}}{{{\text{Cost}}\,{\text{Price}}}} \times 100\% $
So, substitute $\dfrac{{4x}}{5}$ for Selling Price and $12\% $ for Profit Percent and find the value of Cost Price in the terms of x.
$
  12\% = \dfrac{{\dfrac{{4x}}{5} - {\text{Cost}}\,{\text{Price}}}}{{{\text{Cost}}\,{\text{Price}}}} \times 100\% \\
  \dfrac{{12}}{{100}} = \dfrac{{\dfrac{{4x}}{5} - {\text{Cost}}\,{\text{Price}}}}{{{\text{Cost}}\,{\text{Price}}}} \\
  0.12 \times {\text{Cost}}\,{\text{Price}} = \dfrac{{4x}}{5} - {\text{Cost}}\,{\text{Price}} \\
  0.12 \times {\text{Cost}}\,{\text{Price}} + {\text{Cost}}\,{\text{Price}} = \dfrac{{4x}}{5} \\
  1.12{\text{Cost}}\,{\text{Price}} = \dfrac{{4x}}{5} \\
  {\text{Cost}}\,{\text{Price}} = \dfrac{{4x}}{5} \times \dfrac{1}{{1.12}} \\
  {\text{Cost}}\,{\text{Price}} = \dfrac{{5x}}{7} \\
 $
Therefore, the cost price of an article is $\dfrac{{5x}}{7}$.
Again, it is given that the overall gain is Rs. 135.
As, ${\text{Gain}} = {\text{Selling}}\,{\text{Price}} - {\text{Cost}}\,{\text{Price}}$
So, substitute $\dfrac{{5x}}{7}$ for cost price and $\dfrac{{4x}}{5}$ for selling price and 135 for gain and calculate the value of x.
$
  {\text{Gain}} = {\text{Selling}}\,{\text{Price}} - {\text{Cost}}\,{\text{Price}} \\
  {\text{135 = }}\dfrac{{4x}}{5} - \dfrac{{5x}}{7} \\
  135 = \dfrac{{28x - 25x}}{{35}} \\
  135 \times 35 = 3x \\
  x = \dfrac{{4725}}{3} \\
  x = 1575 \\
 $
Therefore, the advertised price of an article is Rs. 1575.
Additional Information:
The advertised price is also known as the market price.
If the selling price is more than the cost price then it is the condition where a person is in profit and when the cost price is more than the selling price then it is a case of loss.

Note:
In this case, if we assume some value for the advertised price or marked price, we can easily interpret its value, here in this question we have assumed it to be x, as it is given in the question the sellers sell his goods at $20\% $ discount, then the advertised price and that would be the selling price and we can use the formula of profit percentage to get the value of cost price and thereafter we can find what would be the value of advertised price by using the formula of gain.