A shopkeeper sells two TVs for ₹$9600$ each. On one he gains $20\%$; on the other he loses $20\%$. What is his net gain or loss on the two transactions?

**Principle.** When two items are sold at the same SP, one at $x\%$ gain and the other at $x\%$ loss, there is always a net loss of $\dfrac{x^2}{100}\%$. **Apply.** $x = 20$, so loss $= \dfrac{400}{100} = 4\%$. **Verification.** CP$_1 = \dfrac{9600}{1.2} = 8000$; CP$_2 = \dfrac{9600}{0.8} = 12000$. Total CP $= 20000$, total SP $= 19200$, so loss $= 800$ on $20000 = 4\%$. **Why option C is wrong.** It's tempting to assume the percentages cancel — but the bases differ. The loss happens because the $20\%$ loss is applied to a *larger* CP than the $20\%$ gain.