Question

The price of a car is lowered by $$20\mathrm{\%}$$ to Rs. 40,000. What was the original price?

Answer 1

Hint: Here, we will first assume the original price and then find the value of the reducing price using the original price. Then calculate the difference of reducing price from the original price of a car and take this difference equal to the reduced price to find the original price.

Complete step-by-step solution
Let us assume that the original price is Rs. $$x$$.

We will first find the value of reducing price of a car lowered by $$20\mathrm{\%}$$ in terms of $$x$$.

$${\displaystyle \frac{20}{100}}x$$

Now we will calculate the original price of a car, which was lowered to Rs. 40,000 by subtracting the reducing price from the original price.
$$\begin{gathered} \Rightarrow x-{\displaystyle \frac{20}{100}}x=40000 \\ \Rightarrow {\displaystyle \frac{100x-20x}{100}}=40000 \\ \Rightarrow {\displaystyle \frac{80x}{100}}=40000 \end{gathered}$$

Multiplying the above equation by 100 on each of the sides, we get

$$\begin{gathered} \Rightarrow {\displaystyle \frac{80x}{100}}\times 100=40000\times 100 \\ \Rightarrow 80x=4000000 \end{gathered}$$

Dividing the above equation by 80 on both sides, we get
$$\begin{gathered} \Rightarrow {\displaystyle \frac{80x}{80}}={\displaystyle \frac{4000000}{80}} \\ \Rightarrow x=50000 \end{gathered}$$

Thus, the original price of a car is Rs. 50000.

Note: In these types of questions, we first assume the original price as any variable and then find the reducing price using the original price. In this question, some students find the sum of the reducing price and original price, which is wrong, we always have to find the difference as the prices are lowered.