Question

A shopkeeper sold a TV set for Rs.17940 with a discount of 8% and earned a profit of 19.6%. What would have been the percentage of profit earned, if no discount was offered?
A. 25%
B. 30%
C. 35%
D. 40%

Answer 1

Hint: Use the formula, $\dfrac{{(100 - discount\% )MarkedPrice}}{{100}} = SellingPrice$ and $C.P. = \dfrac{{100}}{{100 + profit\% }} \times S.P.$ When no discount is offered the marked price is the selling price.

Complete step-by-step answer:
Given, Discount = 8%
Selling Price (S.P.) = Rs. 17940
Let the marked price be Rs. x
Using equation, $\dfrac{{(100 - discount\% )MarkedPrice}}{{100}} = SellingPrice$, put the values given in the question we get
$
  \dfrac{{92x}}{{100}} = 17940 \\
   \Rightarrow x = \dfrac{{1794000}}{{92}} = Rs.19500 \\
$
Now given Profit is 19.6%.
S.P. is Rs.17940
Using, $C.P. = \dfrac{{100}}{{100 + profit\% }} \times S.P.$
$\therefore C.P. = \dfrac{{100}}{{119.6}} \times 17940 = Rs.15000$
If no discount was offered then
$
  C.P. = Rs.15000, S.P. = Rs.19500 \\
  \therefore Profit = S.P. - C.P. \\
   \Rightarrow \Pr ofit = 19500 - 15000 = Rs.4500 \\
$
Therefore, $
  Profit\% = \dfrac{{Profit}}{{C.P.}} \times 100 \\
    \\
 $
So, $
  Profit\% = \dfrac{{4500}}{{15000}} \times 100 = 30\% \\
    \\
$
Hence, the profit earned if no discount was offered is 30%, Option (B) is correct.

Note: Whenever such type of question appears, first write all the things given in the question and then find the marked price by using the formula, $\dfrac{{(100 - discount\% )MarkedPrice}}{{100}} = Selling Price$ and then step by step put the values given in the question in the equations used to find the answer. Finally use the standard equation to find the profit earned.