A man's wage was reduced by 50%. Again the reduced wage was increased by 50%. Find his loss in terms of percentage.

Question

A man's wage was reduced by 50%. Again the reduced wage was increased by 50%. Find his loss in terms of percentage.

1. A. 25% (Correct answer)
2. B. 30%
3. C. 20%
4. D. 35%

Correct Answer

Option A — 25%

Detailed Solution & Explanation

The correct answer is 25%.

Key Points

• Take the original wage as 100.
• After a 50% cut it becomes 50.
• A 50% rise on 50 adds 25, giving 75.
• The loss is 100 − 75 = 25, so the loss is 25%.
• A percentage decrease followed by an equal percentage increase never restores the original value, because the increase applies to a smaller base.

Additional Information

• For two successive percentage changes the net effect is x + y + (xy/100), taking decreases as negative.
• Here: −50 + 50 + (−50 × 50)/100 = −25, confirming the 25% loss directly.
• A general result worth remembering: an equal percentage decrease followed by an equal percentage increase always ends below the original, because the rise is applied to a smaller base. The same holds in reverse order.
• The loss for an equal x% down-then-up is always x²/100 percent — here 50²/100 = 25%.