Question

By selling an article for Rs. 810, a loss of 10% is suffered. Find its cost price

Answer 1

Hint: Take the cost of an article by a variable then find the value of the loss suffered by the merchant and then finally add the loss price with the Cost price and equate it with the selling price given.

Complete step-by-step solution:
Let us take an variable which is the cost price of the article, let it be as x
It is given that a loss of $10\%$ was suffered
Therefore the loss price will be \[x \times 10\% = x \times \dfrac{{10}}{{100}} = \dfrac{x}{{10}}\]
Now we know that cost price + loss = sell price
Which means that \[x - x \times 10\% = 810\]
So by solving we will get
\[\begin{array}{l}
\therefore x - x \times 10\% = 810\\
 \Rightarrow x - \dfrac{x}{{10}} = 810\\
 \Rightarrow \dfrac{{10x - x}}{{10}} = 810\\
 \Rightarrow 9x = 810 \times 10\\
 \Rightarrow 9x = 8100\\
 \Rightarrow x = \dfrac{{8100}}{9}\\
 \Rightarrow x = 900
\end{array}\]
Which means that the cost price was RS. 900.

Note: It should be noted that, if cost price is denoted as CP and sell price as SP then \[\text{loss} = SP - CP \] and \[\text{profit} = CP - SP\] that's why here when the SP was given i have just converted the equation to \[\text{loss} + CP = SP\] .