Q.A person sells two watches for ₹960 each. On one he gains 20% and on the other he loses 20%. Find his overall gain or loss percentage.

Find each cost price separately from the common selling price, then compare total cost with total selling price — selling two items at the same price with equal gain and loss percentages always ends in a net loss.

$CP_1=800$, $CP_2=1200$; total $CP=2000$, total $SP=1920$; loss $=80$, i.e. $\dfrac{80}{2000}\times100=4\%$.

Each watch sells for $SP=₹960$; the first at $20\%$ gain, the second at $20\%$ loss. The two cost prices differ and must be found separately.

Step 1 — Cost price of the first watch (20% gain).

Step 2 — Cost price of the second watch (20% loss).

Step 3 — Compare totals.

Since total $SP<$ total $CP$, there is a loss of $2000-1920=₹80$.

Step 4 — Overall loss percentage.

Check (independent verification / shortcut). Whenever two articles are sold at the same price, one at $x\%$ gain and the other at $x\%$ loss, there is always a net loss of $\dfrac{x^2}{100}\%$. Here $\dfrac{20^2}{100}=\dfrac{400}{100}=4\%$, confirming the result.

Direct-formula method: for equal gain and loss percentages $x$ on the same selling price, the net result is always a loss of $\dfrac{x^2}{100}\%$. With $x=20$, the loss is $\dfrac{400}{100}=4\%$, without needing the individual cost prices.

The tempting but wrong conclusion is that a 20% gain and a 20% loss cancel to no profit and no loss. They do not, because the two percentages sit on different cost prices — the loss is taken on the costlier watch, so the deal ends in a net 4% loss.