Question

A shopkeeper sells 25 articles at Rs 45 per article after giving 10% discount and earns 50% profit if the discount is not given the profit gained is
A. $60\% $
B. $60\dfrac{2}{3}\% $
C. $66\% $
D. $66\dfrac{2}{3}\% $

Answer 1

Hint-In this question, selling price of articles is given to us (10% discount included) Find the marked price of each article and cost price (using given profit percentage) and directly calculate the profit without discount.

Complete step-by-step answer:

Let marked price of each article $ = Rs{\text{ }}x$

Given, selling price of each article after 10% discount $ = Rs{\text{ }}45$

Now, selling price = $90\% {\text{ }}of{\text{ }}x$

$

  45 = \dfrac{{90}}{{100}} \times x \\

  x = \dfrac{{45 \times 100}}{{90}} \\

  x = 50 \\

$

Marked price = Rs 50

Now, cost price

$

   = \dfrac{{100}}{{150}} \times 45 \\

   = Rs{\text{ }}30{\text{ }}[\because 50\% {\text{ profit]}} \\

$

When no discount is given

Cost price = Rs 30

Selling price = Rs 50

Profit obtained

$

   = \dfrac{{50 - 30}}{{50}} \times 100 \\

   = 66\dfrac{2}{3}\% \\

$

Hence, the correct option is D.

Note- In order to solve such problems related to profit and loss with conditions students must try to find profit and loss or percentage as asked separately for both the cases. These problems can also be solved by using the direct formula method but those methods should only be used in competitive exams as they are a bit troublesome to remember.