Question

A man sold two mobile phones at 4,500 each. He sold one at a loss of 15% and the other at a gain of 15%. His loss or gain is........

• A. 15% gain
• B. 15% loss
• C. 2.25% gain
• D. 2.25% loss

Answer 1

Answer:

D. 2.25% loss

Quick Trick Method (Percentage Loss)

When two items are sold at the same selling price, one at a gain of $x\%$ and the other at a loss of $x\%$, there is always a net loss. The formula for the net loss percentage is:
$\text{Loss } \% = \left(\frac{x}{100}\right)^2 \times 100 = \frac{x^2}{100}$

Substituting $x = 15$:
$\text{Loss } \% = \frac{15^2}{100} = \frac{225}{100} = \mathbf{2.25\%}$