A man marks his goods at a price that would give him $20 \%$ profit. He sells $\displaystyle \frac{3}{5}$ of the goods at the marked price and sells the remaining at $20 \%$ discount. Find his gain per cent on the whole transaction.

Assuming the cost price is 100, the marked price is 120, and the total cost for all goods is 100. He sells three-fifths at 120, which is 72, and sells the remaining two-fifths at a 20 percent discount, which is 120 times 0.8 times 0.4, equaling 38.4. The total selling price is 72 plus 38.4, which is 110.4, so the gain percent is 10.4 percent.

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