Question

A man sells s Scooter for Rs. 18000 making a profit of $ 20\% $ how much did the scooter cost him? \[\]

Answer 1

Hint: We assume cost price to be $ \text{CP}=x $ rupees. We use the formula for profit percentage $ \%\text{Profit}=\dfrac{\text{Profit}}{\text{CP}}\times 100=\dfrac{\text{SP}-\text{CP}}{\text{CP}}\times 100 $ and put given values of percentage profit, selling price and unknown cost price as $ x $ . We solve for $ x $ to get the answer. \[\]

Complete step by step answer:
We know that cost price abbreviated as CP of an article is the price at which is the article is bought or the price that was spent for making the article from materials plus additional expenditure. The additional expenditure may be taxes, transportation, repairs etc. \[\]
The selling price abbreviated as SP is the price at which the article is sold. If selling price is greater than cost price then we say the sellers earned profit or gain. The profit amount is given by
\[\text{Profit}=\text{SP}-\text{CP}\]
The percentage profit is calculated on cost price as
\[\%\text{Profit}=\dfrac{\text{Profit}}{\text{CP}}\times 100=\dfrac{\text{SP}-\text{CP}}{\text{CP}}\times 100\]
We are give in the question that A man sells s scooter for 18000 rupees making a profit of $ 20\% $ . So we have $ \text{SP}=18000,\%\text{Profit}=20 $ . We assume the price of the scooter as $ x $ rupees and put the known and unknown values in the percentage profit formula to have ;
\[20=\dfrac{18000-x}{x}\times 100\]
We divide both sides in the above step by 20 to have;
\[\Rightarrow 1=\dfrac{18000-x}{x}\times 5\]
We multiply both sides in the above step by $ x $ to have;
\[\begin{align}
  & \Rightarrow x=\left( 18000-x \right)\times 5 \\
 & \Rightarrow x=18000\times 5-5x \\
 & \Rightarrow 6x=18000\times 5 \\
\end{align}\]
 We divide both sides in the above step by 20 to have;
\[\Rightarrow x=\dfrac{18000\times 5}{6}=3000\times 5=15000\]
So the scooter cost the man Rs.15000. \[\]

Note:
 We note that the selling price is less than the cost price then we say the seller has caused the loss. The loss amount is given by $ \text{Loss}=\text{CP}-\text{SP} $ .The percentage loss is calculated on cost price as $ \%\text{Loss}=\dfrac{\text{Loss}}{\text{CP}}\times 100 $ . We directly find the cost price using the following formula $ \text{CP}=\dfrac{\text{SP}\times 100}{\left( 100+\%\text{Profit} \right)} $ . We must be careful that percentage profit and loss are calculated on cost price not selling price unless motioned otherwise.