Question

If Rajesh sells a scooter to Rahim at a loss of 9% and Rahim sells the scooter at a profit of 5% which sums up to a total of Rs. 14,490. Find the cost price and selling price of the scooter for Rajesh.

Answer 1

Hint: In order to find the CP and SP of the scooter for Rajesh, we have to first compute the cost price of Rahim using the profit percent and selling price of Rahim. This cost price of Rahim is the selling price of Rajesh at 8% loss, which is used to find the cost price of Rajesh. We use the formula of profit percent and loss percent.

Complete step by step solution:
Given Data,
Selling price of Rahim is 14,490/-
Profit percentage – 5%
Using the SP and gain percent of Rahim, let us find the CP of Rahim.
We know the formula of Profit Percent is given by, ${\text{Profit % = }}\dfrac{{{\text{SP - CP}}}}{{{\text{CP}}}} \times 100$
Therefore Cost Price of Rahim is determined as follows:
$
   \Rightarrow {\text{5 = }}\dfrac{{{\text{14490 - CP}}}}{{{\text{CP}}}} \times 100 \\
   \Rightarrow 14490{\text{ }} - {\text{ CP = 0}}{\text{.05CP}} \\
   \Rightarrow 14490{\text{ = 1}}{\text{.05CP}} \\
   \Rightarrow {\text{CP = Rs 13,800}} \\
$
Thus the Cost Price of Rahim is 13,800/- which is nothing but the selling price of Rajesh, as it is given that Rajesh sold the bike to Rahim at 9% loss.
Using the given let us determine the cost price of Rajesh, which is as follows:
The formula of loss percent is given by, ${\text{Loss % = }}\dfrac{{{\text{CP - SP}}}}{{{\text{CP}}}} \times 100$
$ \Rightarrow 9{\text{ = }}\dfrac{{{\text{CP - 13800}}}}{{{\text{CP}}}} \times 100$
$ \Rightarrow {\text{CP - 13800 = 0}}{\text{.09CP}}$
$ \Rightarrow {\text{13800 = 0}}{\text{.92CP}}$
$ \Rightarrow {\text{CP = Rs}}{\text{. 15000}}$
Therefore the cost price and selling price of Rajesh for the scooter is Rs. 15,000 and Rs. 13,800 respectively.

Note: In order to solve this type of problems the key is to the concept of profit, loss, gain percent and loss percent and their respective formulae. We define profit as the difference between selling price and cost price. Profit percent is nothing but profit expressed per hundred. Loss is defined as the difference between cost price and selling price and loss percent is loss expressed per hundred.
The formulae of profit and loss percent has to be known in order to solve this type of question. We have to do a precise calculation to determine the answer.