Question

A pre-owned car show-room owner bought a second-hand car for Rs.150000. He spent Rs.20000 on repairs and painting then sold it for Rs.200000. Find whether he gets profit or loss. If so, what percent?

Answer 1

Hint: To solve this question, we will first of all calculate the actual CP (cost price) by adding the given CP to 20000 (the money he used on painting and repair). Then, we will obtain actual CP by it. Then, profit and profit % can be calculated using formula \[\text{Profit = SP-CP and Profit }\!\!\%\!\!\text{ = }\dfrac{\text{Profit}}{\text{CP}}\times 100\]
Where, SP = selling price and CP = cost price.

Complete step by step answer:
Given the old cost price CP of car is CP = Rs.150000 and the selling price of car is SP = Rs.200000.
Now, as he invested Rs.20000 on repairs and painting. Therefore, Rs.20000 should be also counted in cost price CP of car.
So, new cost price CP of car = old CP + Rs.20000
\[\begin{align}
  & \text{CP new}=150000+20000 \\
 & \Rightarrow 170000 \\
\end{align}\]
Therefore, the actual cost price of car is Rs.170000
Profit earned can be calculated by the formula given below:
Profit = Selling price - Cost price (actual)
Substituting the value of selling price, cost price (actual) in above equation, we get:
\[\begin{align}
  & \text{Profit}=200000-170000 \\
 & \Rightarrow 30000 \\
\end{align}\]
Therefore, he earned a profit of Rs.30000
So, we have obtained that, the man is getting profit from the scenario, as profit value is positive.
Now, we have to finally calculate profit %.
It can be calculated using formula stated below:
\[\text{Profit }\!\!\%\!\!\text{ = }\dfrac{\text{Profit}}{\text{CP}}\times 100\]
Substituting value of profit and CP in above, we get:
\[\begin{align}
  & \text{Profit }\!\!\%\!\!\text{ = }\dfrac{\text{30000}}{\text{170000}}\times 100 \\
 & \Rightarrow \dfrac{3}{17}\times 100 \\
 & \Rightarrow 17.647\% \\
\end{align}\]

Therefore, he is getting profit of Rs.30000 and his profit % is 17.647%

Note: Another way to solve this question is by first calculating profit by SP - CP (old)
\[\begin{align}
  & \text{Profit = }200000-150000 \\
 & \Rightarrow \text{50000} \\
\end{align}\]
Now, as he had used Rs.20000 in repairs, so we will subtract it from profit.
\[\begin{align}
  & \text{Actual profit}=50000-20000 \\
 & \Rightarrow 30000 \\
\end{align}\]
Anyway the answer of profit and profit % is the same.