Question

By selling an article for Rs. 96 a man earns a profit of as much percent as the cost price of an article. The cost of one dozen of such article is
A) ${\text{Rs}}{\text{. 650}}$
B) ${\text{Rs}}{\text{. 700}}$
C) ${\text{Rs}}{\text{. 720}}$
D) ${\text{Rs}}{\text{. 750}}$

Answer 1

Hint: To solve this question, first we need to evaluate the value of cost price of a single article which can be found by using the formula of profit ( \[profit{\text{ }}\% = \dfrac{{\left( {selling{\text{ }}price - {\text{ }}cost{\text{ }}price} \right)}}{{cost{\text{ }}price}}\] ) and condition given in the question.

Complete step-by-step answer:
Given that Selling price is 96 rupees
Let the cost price of article be ${\text{Rs}}{\text{. }}x$
Profit will also be $x\% $
The profit percentage is given by
\[
  profit{\text{ }}\% = \dfrac{{\left( {selling{\text{ }}price - {\text{ }}cost{\text{ }}price} \right)}}{{cost{\text{ }}price}} \\
   \Rightarrow \dfrac{x}{{100}} = \dfrac{{96 - x}}{x} \\
   \Rightarrow {x^2} = 9600 - 100x \\
   \Rightarrow {x^2} + 100x - 9600 = 0 \\
 \]
Solving the above quadratic equation using factorization method
$
   \Rightarrow {x^2} + 160x - 60x - 9600 = 0 \\
   \Rightarrow x(x + 160) - 60(x + 160) = 0 \\
   \Rightarrow (x - 60)(x + 160) = 0 \\
  x = 60{\text{ }}or{\text{ }}x = - 160 \\
$
Neglecting the negative value of x as cost price is not negative.
Cost price of one article is 60 rupees.
Cost price of one dozen of such article will be
$(12 \times 60) = {\text{Rs}}{\text{. 720}}$
Hence, correct option is “C”

Note: In order to solve these types of questions, remember the formulas of profit and loss. Also remember some terms such as Cost price- the price at which article is purchased, marked price – the price written on the article, selling price- the price at which article is sold.