A trader allows a discount of 20% of his goods and still

makes at profit of 25%. Find the profit % made, if he sells his
good at (i) Marked price (ii) at 10% discount.

To find the profit percentage made by the trader, we need to know the cost price of the goods.

Let's assume the cost price (CP) of the goods is $100.

(i) When the trader sells the goods at the marked price:

Given that the trader allows a discount of 20%, it means he sells the goods for 80% of the marked price.

Profit = Selling Price - Cost Price
Profit = 80% of the marked price - $100
Profit = 80/100 * Marked Price - $100

We are also given that the trader makes a profit of 25%, so we can write the equation:

Profit = 25% of the Cost Price
Profit = 25/100 * $100

Now, we can equate both the profit expressions and solve for the Marked Price:

80/100 * Marked Price - $100 = 25/100 * $100

Simplifying the equation:

0.8 * Marked Price - $100 = 0.25 * $100

0.8 * Marked Price = $25 + $100
0.8 * Marked Price = $125

Now, we can solve for the Marked Price by dividing both sides of the equation by 0.8:

Marked Price = $125 / 0.8
Marked Price = $156.25

Profit % = (Profit / Cost Price) * 100
Profit % = ($25 / $100) * 100
Profit % = 25%

Therefore, when the trader sells the goods at the marked price, he makes a profit of 25%.

(ii) When the trader sells the goods at a 10% discount:

Given that the trader sells the goods at a 10% discount, it means he sells the goods for 90% of the marked price.

Profit = Selling Price - Cost Price
Profit = 90% of the marked price - $100

We need to again equate the profit expression with the profit percentage:

90% of the marked price - $100 = 25% of the Cost Price
0.9 * Marked Price - $100 = 25/100 * $100

Simplifying the equation:

0.9 * Marked Price = $25 + $100
0.9 * Marked Price = $125

Now, we can solve for the Marked Price by dividing both sides of the equation by 0.9:

Marked Price = $125 / 0.9
Marked Price ≈ $138.89

Profit % = (Profit / Cost Price) * 100
Profit % = ($25 / $100) * 100
Profit % = 25%

Therefore, when the trader sells the goods at a 10% discount, he still makes a profit of 25%.