Question

A shopkeeper sells an article at a loss of $12\dfrac{1}{2}\% $, had he sold it for Rs. $51.80$ more than he would have earned a profit of $6\% $. Then cost price of the article is
A. Rs.$280$
B. Rs. $300$
C. Rs. $380$
D. Rs. $400$

Answer 1

Hint: In this problem, we have given that a shopkeeper sells an article at a loss of some percentage then the shopkeeper sold an article for a certain rupees more that he would have earned profit for some percentage. Now our aim is to find the cost price of the article.

Complete step-by-step solution:
Let the cost price be Rs.$x$
An article at a loss of $12\dfrac{1}{2}\% $ means selling price of $100\% - 12.5\% = 87.5\% $
Then, $\left( {106\% {\text{ of }}x} \right) - \left( {87.5\% {\text{ of }}x} \right) = 51.80$
$ \Rightarrow 18\dfrac{1}{2}\% {\text{ of }}x = 51.80$
In the above step we have a mixed fraction, and then we have $\dfrac{{37}}{2}\% x = 51.80$
$ \Rightarrow x = \dfrac{{51.80 \times 100 \times 2}}{{37}}$
Hence,
$ \Rightarrow x = Rs.280$

$\therefore $ The cost price of an article is $Rs.280$.

Note: The amount paid to purchase an article or the price at which an article is made is known as its cost price. The price at which an article is sold is known as its selling price. The cost of the product is the cost of producing the product and is the price at which the seller is purchasing the goods. Market price is the price at which the seller is selling the goods. This is the difference between cost price and selling price.
A whole number and a fraction combined into one mixed number is a mixed fraction. In this problem also we faced a mixed fraction number and we converted it into a simple fractional number by multiplying the whole number with the denominator and adding it to the numerator then we got a simple fractional number.