Correct Answer: 28.8%

Solution : Let the cost price of 1 kg of goods be Rs. 100.
Let the total goods be 100 kg.
$\therefore$ Total cost price of 100 kg of goods = 100 × 100 = 10000
The marked price of 1 kg of the goods = 100 + 40 = 140
He sells $\frac{1}{5}$ th of his goods at a discount of 10%.
$\frac{1}{5}$ th of his goods = $\frac{1}{5}×100=20$ kg
$\therefore$ The total price of 20 kg of goods = $(\frac{100-10}{100}×140)×20=126×20=2520$
He sells half of the goods at the marked price.
$\therefore$ Total price of half of the goods = $\frac{100}{2}×140=7000$
He sells the rest of the goods at a discount of 20%.
Amount of goods left = 100 – 20 – 50 = 30 kg
$\therefore$ Total price of 30 kg of goods = $(\frac{100-20}{100}×140)×30=112×30=3360$
Total selling price = 2520 + 7000 + 3360 = 12880
$\therefore$ Profit percentage = $\frac{\text{Selling price – Cost price}}{\text{Cost price}}×100=\frac{12880-10000}{10000}×100=28.8\%$
Hence, the correct answer is 28.8%.