Question

Bala sells a car at 5% profit for Rs. 210000. If he sells it for Rs. 218000 then what will be his profit percentage?

Answer 1

Hint: We first need to assume the cost price of the car as a variable. From the 5% profited selling price of Rs. 210000, we find the cost price. Then we find the profit if he wants to sell the car for Rs. 218000. We also find the profit percentage to complete the solution.

Complete step by step answer:
Let the cost price of the car be Rs. $x(x>0)$.
Bala sells it at 5% profit for Rs. 210000. This means at 5% increased value over Rs. x will be Rs. 210000.
Expressing mathematically, we get $x(1+{\displaystyle \frac{5}{100}})=210000$.
Solving the equation, we get
$\begin{array}{rl}& \Rightarrow x\left({\displaystyle \frac{21}{20}}\right)=210000\\ & \Rightarrow x={\displaystyle \frac{20\times 210000}{21}}=200000\end{array}$
So, the cost price of the car is Rs. 200000.
Now he wants to sell for Rs. 218000. The profit will be Rs. $$218000-200000=18000$$.
The profit percentage will be $\Rightarrow x={\displaystyle \frac{18000\times 100}{200000}}=9$.

Therefore, if Bala sells it for Rs. 218000 then his profit percentage will be 9.

Note: We could have used the concept of base value of 100. We would have imagined the cost price as 100 instead of a variable. Then the 5% profited value would have been 105. This value is similar to Rs. 210000 to find the actual cost price which is similar to 100. Following the same process, we find the profit percentage for Rs. 218000.