The price of an item is first reduced by 25 percent. By what percentage must the reduced price be increased to obtain the original price again?

Introduction / Context:
This question checks understanding of successive percentage changes. A decrease followed by an increase does not lead back to the starting value when the percentages are numerically equal, because the bases are different. This is a very standard trap in aptitude tests.

Given Data / Assumptions:

• The original price of an item is reduced by 25 percent.
• We then want to increase the reduced price to get back to the original price.
• We need the required percentage increase on the reduced price.

Concept / Approach:
Percentage decrease and increase act on the current value, not on the original value in both steps. The natural method is to assume a convenient original price, apply the decrease to get the reduced price and then compute the required increase that brings us back to the assumed original price.

Step-by-Step Solution:
Assume original price = 100 units.After a 25 percent decrease, reduced price = 100 - 25 = 75 units.We want to reach back to 100 units from 75 units.Increase required = 100 - 75 = 25 units.Required percentage increase = (25 / 75) * 100 = 33.33 percent (approximately).

Verification / Alternative check:
If the actual original price were Rs. 400, then a 25 percent reduction gives 400 - 0.25 * 400 = Rs. 300. To return from Rs. 300 to Rs. 400, we need an increase of Rs. 100. The percentage is 100 / 300 * 100 = 33.33 percent, which confirms the same value.

Why Other Options Are Wrong:
Values like 43.3 percent, 50 percent and 55.3 percent are obtained when the candidate mistakenly applies the percentage on the wrong base or treats the two percentages symmetrically. They do not convert 75 back to 100, so they cannot be correct.

Common Pitfalls:
The most common mistake is to think that if a quantity is reduced by 25 percent, an increase of 25 percent will bring it back to its original value. This is wrong because the 25 percent increase is applied on the smaller reduced value, not on the original value. Always identify the correct base.

Final Answer:
The reduced price must be increased by approximately 33.33 percent to restore the original price.