Question

A man sells 12 articles for Rs 80 gaining $33\dfrac{1}{3}\%$. Find the number of articles bought by a man for Rs 90.

Answer 1

Hint: We have the selling price of 12 articles and the profit percentage gained from it. We will calculate the profit using the profit percentage Then we will use the relation between the selling price, profit and cost price to find the cost price of 12 articles. We will get the cost price of one article from this and we can use it to calculate the number of articles that can be bought using Rs 90.

Complete step by step answer:
A man sells 12 articles for Rs 80 gaining $33\dfrac{1}{3}\%$. We can see that the selling price of 12 articles is Rs 80 and the profit percentage gained from it is $33\dfrac{1}{3}\%$. The profit from the profit percentage can be calculated in the following manner,
$\text{profit }\!\!\%\!\!\text{ = }\dfrac{\text{selling price}-\text{cost price}}{\text{cost price}}\times 100$
Substituting the known values, we get
$33\dfrac{1}{3}=\dfrac{80-\text{cost price}}{\text{cost price}}\times 100$
Simplifying the above equation and solving it for cost price, we get the following
$\begin{align}
  & \dfrac{100}{3}=\dfrac{80-\text{cost price}}{\text{cost price}}\times 100 \\
 & \Rightarrow \dfrac{1}{3}=\dfrac{80-\text{cost price}}{\text{cost price}} \\
 & \Rightarrow \text{cost price}=3\left( 80-\text{cost price} \right) \\
 & \Rightarrow \text{cost price}=240-3\times \text{cost price} \\
 & \Rightarrow \text{4}\times \text{cost price}=240 \\
 & \therefore \text{cost price}=60\text{ Rs} \\
\end{align}$
So, we have the cost price of 12 articles as Rs 60. Therefore, the cost price of 1 article is $\dfrac{60}{12}=5\text{ Rs}$. We have to find the number of articles that are bought using Rs 90. We have the following information,
$\begin{align}
  & 1\text{ article : Rs 5} \\
 & x\text{ articles : Rs 90} \\
\end{align}$
So, the number of articles can be calculated using unitary method as follows,
$90\times 1=5\times x$
Solving for $x$, we have
$\begin{align}
  & x=\dfrac{90}{5} \\
 & \therefore x=18 \\
\end{align}$

Hence, 18 articles can be bought using Rs 90.

Note: We should be familiar with the concept of profit percentage. The calculations should be done explicitly so that we can avoid making minor mistakes in the calculations. The unitary method is the method in which we find the value of one quantity and then multiply it to obtain the value of the required quantity.