The price of a car is increased by 25%. By what percentage must this new price be reduced to restore the original price of the car?

Introduction / Context:
This question illustrates a very important concept in percentages: an increase of a certain percentage followed by a decrease of the same percentage does not bring a value back to its original amount. Instead, the required decrease must be calculated from the increased value. Here, the price of a car first goes up by 25%, and we are asked to find the percentage decrease needed to return to the original price. This idea appears frequently in discount, profit and loss, and price revision problems.

Given Data / Assumptions:

Let the original price of the car be P rupees.
The price is increased by 25%, so the new price becomes 1.25P.
We want to find a percentage decrease x% applied to the new price that will bring it back to P.
After decreasing, the price should again equal P.

Concept / Approach:
When a quantity is increased by a percentage and then decreased, the base for the second operation is the new value, not the original value. Therefore, we must set up an equation where the new price after decrease equals the original price. Algebraically, we multiply the increased price by (1 - x / 100) and set the result equal to the original price P. Solving this equation gives the required percentage decrease. This method generalizes to any similar successive percentage change problem.

Step-by-Step Solution:
Let original price = P.After a 25% increase, new price = P * (1 + 25 / 100) = 1.25P.Let the required percentage decrease be x%.After decreasing, price = 1.25P * (1 - x / 100).This must equal the original price P.So, 1.25P * (1 - x / 100) = P.Divide both sides by P: 1.25 * (1 - x / 100) = 1.Therefore, 1 - x / 100 = 1 / 1.25 = 0.8.So x / 100 = 1 - 0.8 = 0.2.Hence x = 0.2 * 100 = 20%.

Verification / Alternative check:
Take a simple assumed original price, for example P = 100 rupees. After a 25% increase, the new price becomes 125 rupees. If we now decrease 125 by 20%, we subtract 20% of 125 which is 25 rupees. So the new price after reduction is 125 - 25 = 100 rupees, exactly back to the original price. This confirms that the required decrease is 20% and not 25%.

Why Other Options Are Wrong:

24% and 21% would produce final prices different from the original and so do not restore the price exactly.
25% decrease from the increased price of 125 would give 93.75, which is less than the original 100 and therefore incorrect.
18% also fails to bring the price back to the original level and arises from incorrect algebra or mental approximation.

Common Pitfalls:
A very common misconception is to think that a 25% increase followed by a 25% decrease returns to the starting value. This is not true because the base values for the percentage operations are different. Another pitfall is performing calculations directly on percentages without converting them to multiplication factors. Always work with the idea that new value = old value * (1 ± percentage / 100) and carefully set up the equation.

Final Answer:
To restore the original price of the car after a 25% increase, the new price must be reduced by 20%.