Question

An item was sold at 50 with a loss of 5 % . What is the cost price ?

Answer 1

Hint: To calculate the cost price, we will use the formula that is \[\text{Cost price = Selling price}\pm \text{Profit/Loss}\], here Selling price and Loss % is given so first we will calculate Loss from Loss % and then we will calculate the cost price.

Complete step-by-step answer:
Let us assume that the Cost price of the given item be $x$, as loss % is given 5 % , and also
Loss % is always calculated on its Cost price, so now we have,
$\text{Loss}=5\%\times $Cost Price of the given item
$=\dfrac{5}{100}\times \left( x \right)$
After simplifying, we get
$\begin{align}
  & =\dfrac{1}{20}\times x \\
 & =\dfrac{x}{20} \\
\end{align}$
We have been given in the question that the Selling Price = 50.
And we know that Cost price = Selling price + Loss
We can substitute the values as below,
$\Rightarrow x=\left( 50+\dfrac{x}{20} \right)$
Bringing like terms to the same side, we have
$\Rightarrow x-\dfrac{x}{20}=50$
Again, after simplifying we have,
$\begin{align}
  & \Rightarrow \dfrac{20x-x}{20}=50 \\
 & \Rightarrow \dfrac{19x}{20}=50 \\
 & \Rightarrow x=\dfrac{50\times 20}{19} \\
 & \Rightarrow x=52.63 \\
\end{align}$
Hence, Cost price of the given item = 52.63

Note: In order to calculate Loss or Profit, we should keep in mind that Profit or Loss percent are always calculated on its cost price. Also while calculating cost price of an item, must be aware of sign in this formula that is \[\text{Cost price = Selling price}\pm \text{Profit/Loss}\] , so if there is a loss we have to add it to the selling price, whereas if there is a profit we have to subtract it from selling price. Also do the same for finding selling price of an item