Question

Rajesh sold his scooter to Rahim at 8% loss and Rahim in turn sold the same scooter to Prem at 5% gain. If Prem paid Rupees 14490 for the scooter. Find the S.P. and the C.P. of the scooter for Rahim.

Answer 1

Hint: For solving this problem, first we calculate the selling price of a scooter from the given problem statement. By using the gain percentage formula, we can easily calculate the cost price of the scooter for Rahim.

Complete step-by-step answer:
According to the problem statement, Prem paid rupees 14490 for purchasing the scooter from Rahim. So, the selling price of the scooter will be 14490.
Since, the gain percent on selling the scooter is 5. So, converting the gain percent to decimal, we obtain 0.05. The formula for gain percent would be expressed as: $\text{Gain percent = }\dfrac{\text{Selling price - Cost price}}{\text{Cost price}}$
Now, putting the value of gain percent and selling price of the scooter in the above expression, we get
$\begin{align}
  & 0.05=\dfrac{14490-CP}{CP} \\
 & 0.05CP=14490-CP \\
 & 1.05CP=14490 \\
 & CP=\dfrac{14490}{1.05} \\
 & CP=13800 \\
\end{align}$
Therefore, the cost price of the scooter is Rs. 13800
The selling price of the scooter is Rs. 14490.

Note: The key concept involved in solving this problem is the knowledge of gain percent on selling an article. Students must be careful while calculating the selling price and cost price by using the gain percent not the loss percent. Also, the gain percent must be converted to decimal.