Question

By selling a scooter for Rs. 9200, a man gains 15%. Find the cost price of the scooter.

Answer 1

Hint: If we want to solve this question, we need to understand about selling price, cost price, profit and profit%. For solving this question, first of all we will assume the cost price of the scooter to be x. Then, we will make an equation with the relation between profit, profit% and the cost price. Then we will compare the equation with another equation with the relation between selling price, cost price and profit. As a result of comparing both the equations, we will get the cost price of the scooter. This will be our final result.

Complete step-by-step answer:
The relation between profit, profit% and cost price is,
\[profit=\dfrac{profit\%}{100}\times \text{cost price}\]
The relation between selling price, cost price and profit is,
\[\text{selling price}=\text{cost price}+\text{profit}\]

Now, we will solve the complete question. As mentioned, we assumed that the cost price of the scooter is x.
According to the question, the values given in the question are,
The selling price of the scooter S.P. \[=9200\]
The percentage of profit gained by the man \[=15\%\]
According to the relation between profit, profit% and cost price,
\[\begin{align}
 & \Rightarrow profit=\dfrac{profit\%}{100}\times \text{cost price} \\
 &\Rightarrow profit=\dfrac{15}{100}\times x \\
 & \Rightarrow profit=\dfrac{3}{20}x \\
\end{align}\]
We got an equation with two unknowns, so now we need to form another equation with the same unknowns so that we can solve them and find our answer.
Another equation can be formed with the relation between selling price, cost price and profit,
The equation which will be formed will be,
\[\begin{align}
& \Rightarrow \text{selling price}=\text{cost price}+\text{profit} \\
& \Rightarrow 9200=x+profit \\
\end{align}\]
Now, if we put the value of profit from the first equation to the second equation, this will be an easier way to solve the equation.
So, after putting the value of profit from first equation to second equation, the resultant equation formed will be,
\[\begin{align}
& \Rightarrow 9200=x+profit \\
& \Rightarrow 9200=x+\dfrac{3}{20}x \\
& \Rightarrow 9200=\dfrac{20x+3x}{20} \\
& \Rightarrow 9200\times 20=23x \\
& \Rightarrow x=8000 \\
\end{align}\]
Hence, the value of cost price of the scooter which we wanted to find out is Rs. 8000

Note: There are so less chances of error in this question, but if the student forgets any of the two relations partially or completely, then the student will have to face a lot of trouble in the solution of this question. Also be careful in putting the value of profit from first equation to second equation, because sometimes a student confuses and puts the value of cost price, which will make the solution lengthier.