A merchant marks up the price of his goods by 40% more than the cost price. He then sells $\frac{1}{5}th$ of his goods at a discount of 10%, half of the goods at the marked price and the rest of the goods at a discount of 20%. Find his profit percentage.

28.8%

Let the CP = 100x

Then the MP = 140x

One fifth of the goods sold at 10% discount means,

= \(\frac{140x × 9}{5 × 10}\) = 25.2x

Half of the goods sold at marked price means = 70x

Remaining = 140x - 28x - 70x = 42x

Now 42x is sold at 20% discount so the selling price of 42X is = 80% of 42x = 33.6x

Total Selling price of all the parts = 25.2x + 70x + 33.6x = 128.8x

So, the profit = 128.8x- 100x = 28.8%