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

Let the original wage be ₹100.

The wage is reduced by 50%:

Loss $= 50\% \text{ of } 100$

$= \dfrac{50}{100} \times 100$

$= 50$

Wage after reduction $= 100 - 50 = 50$

---

The reduced wage is increased by 50%. This increase is calculated on the current wage of ₹50, not the original wage:

Increase $= 50\% \text{ of } 50$

$= \dfrac{50}{100} \times 50$

$= 25$

Final wage $= 50 + 25 = 75$

---

The loss in wage:

Loss $= 100 - 75 = 25$

Loss percentage $= \dfrac{\text{Loss}}{\text{Original Wage}} \times 100$

$= \dfrac{25}{100} \times 100$

$= 25\%$

---

The 50% decrease is calculated on ₹100 (loses ₹50), while the 50% increase is calculated on ₹50 (gains only ₹25). This results in a net loss of ₹25, which is 25% of the original wage.

Alternatively, using the formula for successive percentage changes:

Net percentage change $= a + b + \dfrac{ab}{100}$

where $a = -50$ (decrease) and $b = 50$ (increase)

$= -50 + 50 + \dfrac{(-50)(50)}{100}$

$= 0 - 25$

$= -25\%$

The negative sign indicates a loss of 25%.