Question

The cost price of a flower vase is $Rs\,120$. If the shopkeeper sells it at a loss of $10\% $, find the price at which it was sold.

Answer 1

Hint: The given question revolves around the topic and concepts of profit and loss. The question deals with first purchasing some goods at a cost price, then selling it for a loss of a specific percentage on the cost price of the product. We will first find out the loss in the transaction and then find the selling price using the formula: ${\text{Selling Price = }}\left( {{\text{Cost}}{\text{Price}}} \right) - \left( {{\text{Loss}}} \right)$

Complete step-by-step solution:
The cost price of the flower vase is $Rs\,120$.
Now, we are also provided that the vase is sold for a loss of $10\% $.
We know that the loss percent is always calculated over the cost price of a good. So, we can calculate the loss in the transaction by calculating $10\% $ of $Rs\,120$.
So, we get the loss incurred as,
\[Loss = \dfrac{{Percentage}}{{100}} \times {\text{Cost}}\,{\text{price}}\]
So, substituting the known values, we get,
\[ \Rightarrow Loss = \dfrac{{10}}{{100}} \times {\text{Rs}}\,{\text{120}}\]
Cancelling the common factors, we get,
\[ \Rightarrow Loss = {\text{Rs}}\,{\text{12}}\]
So, the shopkeeper has incurred a loss of \[{\text{Rs}}\,{\text{12}}\].
Now, we have the formula for Selling price as ${\text{Selling Price = }}\left( {{\text{Cost}}{\text{Price}}} \right) - \left( {{\text{Loss}}} \right)$ when cost price and loss is known to us. So, we get,
${\text{Selling Price = Rs}}\,{\text{120}} - {\text{Rs}}\,{\text{12}}$
Simplifying the calculations, we get,
$ \Rightarrow {\text{Selling Price = Rs}}\,108$

Note: One must have accuracy in arithmetic so as to solve these types of questions within a limited time frame. We should have a clear understanding of how to find the percentage of a specific number so as to find the gain and loss percent for the goods.