Question

A product costs a company Rs 60 to manufacture. It sold the product to the dealer for Rs 70, who in turn sold it to the shopkeeper for Rs 85, who sold to a customer for Rs 102. What is the percentage of profit for the company and who made the highest profit on selling the product?

Answer 1

Hint: The cost bought by someone is called cost price (C.P) and the cost sold by someone is called selling price (S.P). Then we can calculate the profit percentage by using
\[profit=\dfrac{S.P-C.P}{C.P}\times 100\]. By this we can get a profit percentage of each intermediate.

Complete step-by-step answer:
Let us consider that the cost price of company as
\[{{\left( C.P \right)}_{Company}}=60/-\]
Let us consider the selling price of company as
\[{{\left( S.P \right)}_{Company}}=70/-\]
Now let us calculate the profit percentage as follows
\[\begin{align}
  & \Rightarrow {{P}_{company}}=\dfrac{{{\left( S.P \right)}_{company}}-{{\left( C.P \right)}_{company}}}{{{\left( C.P \right)}_{company}}}\times 100 \\
 & \Rightarrow {{P}_{company}}=\dfrac{70-60}{60}\times 100 \\
 & \Rightarrow {{P}_{company}}=\dfrac{10}{60}\times 100 \\
 & \Rightarrow {{P}_{company}}=16.67 \\
\end{align}\]
So, the company has 16.67 percent of profit.
Now, we know that the selling price of company will be the cost price of dealer

Let us consider that the cost price of dealer as
\[{{\left( C.P \right)}_{dealer}}=70/-\]
Let us consider the selling price of dealer as
\[{{\left( S.P \right)}_{dealer}}=85/-\]
Now let us calculate the profit percentage as follows
\[\begin{align}
  & \Rightarrow {{P}_{dealer}}=\dfrac{{{\left( S.P \right)}_{dealer}}-{{\left( C.P \right)}_{dealer}}}{{{\left( C.P \right)}_{dealer}}}\times 100 \\
 & \Rightarrow {{P}_{dealer}}=\dfrac{85-70}{70}\times 100 \\
 & \Rightarrow {{P}_{dealer}}=\dfrac{15}{70}\times 100 \\
 & \Rightarrow {{P}_{dealer}}=21.43 \\
\end{align}\]
So, dealers have 21.43 percent of profit.
Now we know that the selling price of dealer will be cost price of shopkeeper
Let us consider that the cost price of shopkeeper as
\[{{\left( C.P \right)}_{shopkeeper}}=85/-\]
Let us consider the selling price of shopkeeper as
\[{{\left( S.P \right)}_{shopkeeper}}=102/-\]
Now let us calculate the profit percentage as follows
\[\begin{align}
  & \Rightarrow {{P}_{shopkeeper}}=\dfrac{{{\left( S.P \right)}_{shopkeeper}}-{{\left( C.P \right)}_{shopkeeper}}}{{{\left( C.P \right)}_{shopkeeper}}}\times 100 \\
 & \Rightarrow {{P}_{shopkeeper}}=\dfrac{102-85}{85}\times 100 \\
 & \Rightarrow {{P}_{shopkeeper}}=\dfrac{17}{85}\times 100 \\
 & \Rightarrow {{P}_{shopkeeper}}=20 \\
\end{align}\]
So, the shopkeeper has 20 percent of profit.
Therefore, the profit percentage of the company is 16.67 and clearly we can say that the dealer made the highest profit.

Note: Students will make mistakes in taking the selling price of the company as 102/- which will be wrong. While calculating the percentage of company’s profit some students consider the selling price as 102/- which is wrong. That is the only point in which one can make mistakes.