A number is first increased by 12%, and the increased number is decreased by 8%. Find the net increase or decrease percentage.

Given:

A number is first increased by 12%, and the increased number is decreased by 8%.

Formula used:

Net change percentage = \((x + y + \frac{xy}{100})\)

Where,

x = Percentage increase = 12%

y = Percentage decrease = -8% (negative because it’s a decrease)

Calculations:

Net change percentage = \((x + y + \frac{xy}{100})\)

⇒ Net change percentage = \((12 + (-8) + \frac{12 × (-8)}{100})\)

⇒ Net change percentage = \((12 - 8 - \frac{96}{100})\)

⇒ Net change percentage = \((4 - 0.96)\)

⇒ Net change percentage = 3.04%

∴ The net change is a 3.04% increase, and the correct answer is option (1).