Question

A pre-owned car show-room owner bought a second-hand car for Rs.1,50,000. He spent Rs.20,000 on repairs and painting then sold it for Rs.2,00,000. Find whether he gets profit or loss. If so, in what percentage? \[\]

Answer 1

Hint: We find the cost price (CP) by adding the expenditure of for repairs and painting with the purchasing price of the second-hand car. We see if the cost price is smaller than selling price of the car then we calculate profit amount $\text{Profit}=\text{SP}-\text{CP}$ and percentage profit as $\%\text{Profit}=\dfrac{\text{Profit}}{\text{CP}}\times 100$, otherwise we find the loss amount $\text{Loss}=\text{CP}-\text{SP}$ and percentage loss $\%\text{Loss}=\dfrac{\text{Loss}}{\text{CP}}\times 100$.\[\]

Complete step by step answer:
We know that the cost price abbreviated as CP of an article is the price at which 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 the 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 gain is calculated on cost price as
\[\%\text{Profit}=\dfrac{\text{Profit}}{\text{CP}}\times 100\]
If the selling price is less than cost price then we say the sellers have caused loss. The loss amount is given by;
\[\text{Loss}=\text{CP}-\text{SP}\]
The percentage gain is calculated on cost price as
\[\%\text{Loss}=\dfrac{\text{Loss}}{\text{CP}}\times 100\]
We are given the question that the pre-owned car show-room owner bought a second-hand car for Rs.1, 50,000 and then he spent Rs.20, 000 on repairs and painting. The repairs spending are additional expenditure. Now the cost price of the car is sum of purchasing price and the spending on repairs which is ;
\[\text{CP}=\text{Rs}.150000+\text{Rs}.20000=\text{Rs}.170000\]
We are further given that the owner sold the car for Rs.2,00,000 which means the selling price is ;
\[\text{SP}=\text{Rs}.200000\]
We see that the selling price is greater than the cost price. So the seller has earned profit. So the profit amount is
\[\text{Profit}=\text{SP}-\text{CP}=\text{Rs}.200000-\text{Rs}.170000=\text{Rs}.30000\]

So the profit percentage is
\[\%\text{Profit}=\dfrac{\text{Profit}}{\text{CP}}\times 100=\dfrac{30000}{170000}\times 100=17.64\%\]

Note: We must be careful that the profit percentage or loss percentage are calculated on cost price not on selling price. If there is tax on sales the tax amount has to be added in the selling price. We can find the cost price if selling price and percentage is given as $\text{CP}=\dfrac{\text{SP}\times 100}{100+\%\text{Profit}}$.If selling price and cost price are equal then there is neither profit nor loss.