Question

If a person reduces his selling price of an article by Rs. 40, then the suggested profit of $33\dfrac{1}{3}\% $convert into a loss of 20 %. Find the cost price.

Answer 1

Hint: We will first calculate the relation between the given condition by assuming the cost price to be C, then the new selling price minus reduction of Rs. 40 will be equal to loss in the price value i. e., reduced amount subtracted from the profit made earlier multiplied with the cost price will be equal to the loss faced now multiplied with the cost price.

Complete step-by-step answer:

Let us assume that the cost price of the article be Rs. P and we are given that the selling price when reduced by the shopkeeper, their profit converted into loss.
The person reduced the selling price by Rs. 40.
The profit he used to earn before is $33\dfrac{1}{3}\% $ of the cost price.
The loss that the owner faced is 20% od the total cost price.
We can say that the new selling price minus reduction of Rs. 40 will be equal to the loss in the price value i. e., reduced amount subtracted from the profit made earlier multiplied with the cost price will be equal to the loss faced now multiplied with the cost price.
In terms of an equation, we can write it as $33\dfrac{1}{3}\% C - 40 = 20\% C$ equation(1)$\because 33\dfrac{1}{3}\% = \dfrac{{\left( {33 \times 3} \right) + 1}}{3}\% = \dfrac{{100}}{3}\% $
Converting the percentage into fraction using the formula $x\% = \dfrac{x}{{100}}$, we get
$\dfrac{{\dfrac{{100}}{3}}}{{100}} = \dfrac{1}{3}$ and $20\% = \dfrac{{20}}{{100}} = \dfrac{1}{5}$
We need the profit. So, we can convert this fraction by using the formula $1 + \dfrac{1}{3} = \dfrac{4}{3}$since it is profit and $1 - \dfrac{1}{5} = \dfrac{4}{5}$since it is loss faced and write the equation (1) as:
$ \Rightarrow \dfrac{4}{3}C - 40 = \dfrac{4}{5}C$
Now, simplifying this equation for C, we get
$
   \Rightarrow \dfrac{4}{3}C - \dfrac{4}{5}C = 40 \\
   \Rightarrow \dfrac{8}{{15}}C = 40 \\
   \Rightarrow C = 75 \\
 $
Therefore, the cost price of that article is Rs. 75.

Note: You need to take care of using the right formulae because we were given profit made earlier by the same article and when the selling price is reduced, the loss made by the same article is provided.