Question

A shopkeeper offers a discount of 25% on a T.V and sells it for Rs.8400. What is the cost price of the T.V?
$
  (a){\text{ Rs}}{\text{.8570}} \\
  {\text{(b) Rs}}{\text{.1120}} \\
  {\text{(c) Rs}}{\text{.9040}} \\
  {\text{(d) Rs}}{\text{.8960}} \\
 $

Answer 1

Hint: In this question assume any variable be the cost price of the T.V then use the concept that whatever is the discount, it is on the cost price and use the concept that selling price is the difference of cost price and discount on the cost price to reach the solution of the question.

Complete step-by-step answer:

Let the cost price of the T.V be x Rs.
Now it is given that the shopkeeper offers a discount 25% on a T.V and sells it for Rs. 8400.
So construct the linear equation according to given information.
Therefore the cost price of T.V minus 25% of cost price of T.V is equal to 8400.
$ \Rightarrow x - \dfrac{{25}}{{100}}x = 8400$
Now simplify the above equation we have,
 $ \Rightarrow x - \dfrac{1}{4}x = 8400$
$ \Rightarrow \dfrac{3}{4}x = 8400$
$ \Rightarrow x = \dfrac{{8400 \times 4}}{3} = 2800 \times 4 = 11200$ Rs.
So the cost price of the T.V is 11200 Rs.
Hence option (b) is correct.

Note: Whenever we face such types of problems the key concept is to formulate mathematical equations using the constraints of the discount percentage and selling price. Assumption of the unknown quantity as a variable and formulation of the equation formed in terms of variables helps getting the solution.