Question

A shopkeeper allows a 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 he gains Rs.135.
$
  (a){\text{ Rs}}{\text{.1123}} \\
  (b){\text{ Rs}}{\text{.1395}} \\
  (c){\text{ Rs}}{\text{.1575}} \\
  (d){\text{ Rs}}{\text{.1722}} \\
 $

Answer 1

Hint: In this question let the cost price and advertised piece of the good be two different variables. Use the concept that the selling price must be equal to the advertised price subtracted with the 20% discount of advertised price, and the profit gained is nothing but the selling price subtracted with the cost price.

Complete Step-by-Step solution:
Let the cost price (C.P) of the goods = x Rs.
And let the advertised price of the goods be y Rs.
Now it is given that a shopkeeper allows a 20% discount on the advertised prices.
So the selling price (S.P) of the goods = advertised price – 20% of advertised price
$ \Rightarrow S.P = y - \dfrac{{20}}{{100}}y = \dfrac{4}{5}y$
Now it is that he makes a profit of 12% on the cost price.
As we know profit (P) is the difference between selling price and cost price.
$ \Rightarrow P = S.P - C.P$ …………………. (1)
And profit is 12% of x.
$ \Rightarrow P = \dfrac{{12}}{{100}}x$
Now it is given that he gains 135 Rs.
$ \Rightarrow 135 = \dfrac{{12}}{{100}}x$
Now simplify it and calculate the value of cost price
$ \Rightarrow x = \dfrac{{13500}}{{12}} = 1125$ Rs.
Now from equation (1) we have
$ \Rightarrow P = S.P - C.P$
$135 = \dfrac{4}{5}y - 1125$
Now simplify it and calculate the value of advertised price
$ \Rightarrow \dfrac{4}{5}y = 1125 + 135 = 1260$
$ \Rightarrow y = \dfrac{{1260 \times 5}}{4} = 1575$ Rs.
So the advertised price of the goods is Rs. 1575.
Hence option (C) is correct.

Note: Whenever we face such types of problems it is always advised to use the questions constraints for formulation of equations involving variables. The shopkeeper in this question has two prices to deal with one the actual advertised price but onto that advertised price he gives 20% discount this means that the selling price must be the difference between the two prices that’s how the concept mentioned above in hint has arrived.