Question

A shopkeeper allows a discount of 10% on a watch and still makes a profit of 12%. If the cost price of the watch is Rs. 450, what is its marked price?
$\left( A \right)$ Rs. 540
$\left( B \right)$ Rs. 520
$\left( C \right)$ Rs. 560
$\left( D \right)$ None of these.

Answer 1

Hint – In this particular question assume any variables be the marked price and selling price of the watch later on in the solution use the concept that percentage profit is the ratio of the difference of selling price and cost price to the cost price multiplied by 100 so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Let the marked price of the watch be X Rs.
It is given that the cost price of the watch is = Rs. 450
Now it is given that a shopkeeper allows a discount of 10% on a watch and still makes a profit of 12%.
Let the selling price of the watch be Y Rs.
Now as the shopkeeper earns a profit so the selling price must be greater than the cost price.
So the percentage profit is the ratio of the difference of selling price and cost price to the cost price multiplied by 100.
Now it is given it earns a 12% profit.
Therefore, 12 = $\dfrac{{Y - 450}}{{450}} \times 100$
Now simplify it and calculate the selling price of the watch.
$ \Rightarrow \dfrac{{12\left( {450} \right)}}{{100}} = Y - 450$
$ \Rightarrow Y = 450 + 54 = 504$Rs...................... (1)
Now the discount is on the marked price of the watch.
Now it is given it gives a 10% discount on the marked price so selling price is the difference of the marked price and 10% of marked price,
So after discount the selling price is
Therefore, Y = X – (10/100) X = (9X/10)............. (2)
Now equate equation (1) and (2) we have,
$ \Rightarrow \dfrac{{9X}}{{10}} = 504$
$ \Rightarrow X = \dfrac{{5040}}{9} = 560$ Rs.
So the marked price of the watch is 560 Rs.
So this is the required answer.
Hence option (C) is the correct answer.

Note – Whenever we face such types of questions the key concept we have to remember is that if there is a discount on any product (say n %), then it is on the marked price of the product, so the selling price is the difference of the marked price and n % of marked price, so first calculate the selling price as above then using the discount concept as above and simplify we will get the required answer.