A man’s wages are cut by 50%. Then the reduced wages are increased by 50%. Overall, what percent loss does he suffer relative to his original wages?

Introduction / Context: Opposite percentage changes of the same magnitude do not cancel out because they apply to different bases. A 50% decrease followed by a 50% increase never returns to the starting value.

Given Data / Assumptions:

• Initial wage = W.
• Decrease 50% ⇒ W becomes 0.5W.
• Increase 50% of the reduced wage ⇒ 0.5W * 1.5.

Concept / Approach: Compute the final wage explicitly and compare to the original. The product 0.5 * 1.5 = 0.75 indicates the final is 75% of the original.

Step-by-Step Solution:

Verification / Alternative check: If W = ₹100, new wage after cut = ₹50; after raise = ₹75. Loss = ₹25 ⇒ 25%.

Why Other Options Are Wrong: 0% assumes symmetric cancellation; 0.25% and 2.5% are decimal-place errors.

Common Pitfalls: Adding −50% and +50% to get 0%, forgetting that the 50% increase acts on the reduced base.

Final Answer: 25 %