The price of an article has been reduced by 35 percent. By what percentage must the reduced price now be increased in order to restore the article to its original price?

Introduction / Context:
This question tests understanding of successive percentage changes. A common misconception is that an equal percentage increase will reverse a given percentage decrease, but this is not true because the base values change. Here the price is reduced by 35 percent, and we must find the percentage increase on the reduced price that restores the original price.

Given Data / Assumptions:

• Original price of the article is some amount, say P.
• The price is reduced by 35 percent.
• The reduced price needs to be raised back to the original price.
• We must compute the required percentage increase on the reduced price.
• All changes are based on simple percentage calculations.

Concept / Approach:
Let the original price be P. A reduction of 35 percent means the new price equals 65 percent of P, that is 0.65 * P. To restore the price to P, we need to increase the reduced price up to P. The increase amount is P minus 0.65 * P which is 0.35 * P. The required percentage increase is this increase amount divided by the reduced price, multiplied by 100. This ratio is greater than 35 percent because the base for the increase is smaller than the original price.

Step-by-Step Solution:
Let original price be P rupees.After a 35 percent reduction, the reduced price equals P * (1 minus 0.35) equals 0.65 * P.To restore the original price, we must increase this reduced price back to P.The required increase amount equals P minus 0.65 * P equals 0.35 * P.Required percentage increase equals (increase amount divided by reduced price) multiplied by 100.So percentage increase equals (0.35 * P) / (0.65 * P) * 100.The P cancels, leaving 0.35 / 0.65 * 100.Compute 0.35 / 0.65 equals 35 / 65 which simplifies to 7 / 13, or approximately 0.53846.Thus the required percentage increase is about 0.53846 * 100 equals 53.846 percent, which we write as 53.84 percent.

Verification / Alternative check:
We can choose a simple value for P, for example 100 rupees, to verify. A 35 percent reduction brings the price down to 65 rupees. To get back from 65 rupees to 100 rupees, the increase required is 35 rupees. As a percentage of 65 rupees, this is 35 / 65 * 100 which again gives 53.846 percent. This numerical example confirms the general algebraic derivation.

Why Other Options Are Wrong:
Values 51.8 percent, 49.25 percent, and 47.2 percent all correspond to smaller increases that would not raise the reduced price fully back to the original value. Only 53.84 percent is large enough to convert 65 percent of the original price back to 100 percent. Any smaller percentage would leave the price below the original level.

Common Pitfalls:
A very common error is to say that a 35 percent increase reverses a 35 percent decrease. This is incorrect because the 35 percent decrease is applied on the original price, while the subsequent increase is applied on the reduced price, which is smaller. Another mistake is to compute the difference between 100 and 35 and then use that directly as a percentage without considering the correct base. Always define a variable for the original value and apply percentage changes stepwise to avoid these traps.

Final Answer:
The reduced price must be increased by 53.84 percent to restore the original price.