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# $10\%$ loss on selling price is what percent loss on the cost price?

Last updated date: 24th Mar 2023
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Hint: In the given question, we have to find the percentage of loss on the cost price where the percentage of loss on sale price is already given. We can assume the sale price as $100$ and add the loss to arrive at the cost price. Then we can find the percentage of loss on the cost price by using this percentage formula $p(\% ) = \dfrac{x}{y} \times 100$.

Complete step by step solution:
Let us understand the concept of percent first.
Calculating percentages is a simple mathematical procedure. If you need to find a ratio or a component of a quantity as a proportion of another quantity, you can express it as a percentage.
To find out the percent of a given number, we can use the following formula:
$p(\% ) = \dfrac{x}{y} \times 100$
Where:
$x$= Number for which percentage is to be found out;
$y$= Total or whole number of given data
We can solve the sum as follows:
Let the Sale Price be Rs. $100$
Loss on selling price will be Rs-
$100 \times 10\% = 10$
Now we know that loss is the difference between cost price and selling price. Therefore, we can find the cost price as follows:
$\text{Loss = cost price - selling price}$
Substituting the values, we get,
$100=\text{cost price} - 10$
$\Rightarrow \text{cost price }=100+10=Rs.110$

Now we can find the percentage of loss on cost price with the help of percent formula:
$=\dfrac{\text{Loss (x)}}{\text{Cost price (y)}} \times 100$
$= \dfrac{{10}}{{110}} \times 100$
$= 9.09\%$
Thus, the percentage of loss on cost price will be $9.09\%$.

Note:
In case of profit, the formula is-
$\text{Profit = Selling Price - Cost price}$
We can use the above formula too but will have to use a negative amount when there is loss in place of profit.
For example, the equation in the given sum will be :
$- 10 = 100 - \text{cost price}$
$\text{cost price} = 100 + 10 = 110$