Question

The cost price of a car is Rs.500000. The salesperson marks it $10\%$ above the cost price. Then, the car is sold at a discount of $5\%$. Find the profit and profit percentages.

Answer 1

Hint: Assume the cost price of the car as C.P. and selling price of the car as S.P. Add $10\%$ of 500000 with 500000 to find the marked cost price of the car. Now, consider the discount of $5\%$ and subtract $5\%$ of the marked cost price from the obtained marked cost price to get the value of S.P. Use the formula: - Profit = S.P – C.P and Profit$\%$ = \[\left( \dfrac{S.P.-C.P}{C.P} \right)\times 100\%\] to obtain the answers.

Complete step-by-step solution
Here, let us assume the cost price of the car as C.P. and the selling price of the car as S.P.
Now, it is given that the original cost price of the car is Rs.5000000 but the salesperson marked it $10\%$ above the cost price. So, we have,
Marked cost price of the car = 500000 + $10\%$ of 500000
Marked cost price of the car = 500000 + \[\dfrac{10}{100}\times 500000\]
The marked cost price of the car = 500000 + 50000
The marked cost price of the car = Rs.550000
Now, it is said that the car is sold at a discount of $5\%$. So, the selling price can be given as: -
\[\Rightarrow \] S.P = 550000 – $5\%$ of 550000
\[\Rightarrow \] S.P = 550000 – \[\dfrac{5}{100}\times 550000\]
\[\Rightarrow \] S.P = 550000 – 27500
\[\Rightarrow \] S.P = Rs.522500
Here, the situation is that the salesperson bought the car for Rs.500000 and then he marked the price of the car as Rs.550000. Now, he sold the car at a discount of $5\%$, which is Rs.522500. So, we have,
C.P. = Rs.500000
S.P. = Rs.522500
We know that profit is the difference of S.P. and C.P., so we have,
\[\Rightarrow \] Profit = S.P – C.P
\[\Rightarrow \] Profit = Rs.522500 – Rs.500000
\[\Rightarrow \] Profit = Rs.22500
Now, applying the formula for profit percent we get,
\[\Rightarrow \] Profit$\%$ = (Profit / C.P) \[\times 100\%\]
\[\Rightarrow \] Profit$\%$ = \[\dfrac{22500}{500000}~\times 100\%\]
\[\Rightarrow \] Profit$\%$ = $4.5\%$
Hence, the profit is Rs.22500 and profit$\%$ is $4.5\%$.

Note: One may note that here we do not consider Rs.550000 as C.P. in the calculation for profit because it is the price marked by the salesperson and the actual C.P. of the car is Rs.500000. Now, while calculating the profit percent, remember that we have C.P. in the denominator of the formula. This is because we always consider profit on the cost price. Note that we cannot directly subtract $5\%$ from $10\%$ to get the profit percent as it is a wrong approach.