Raman fixes the sale price of his goods at 16% above the cost price. He sells his goods at 12% less than the fixed price. Find the profit percentage correct to two places of decimal.

The correct option is 2.08%.

Let us solve this problem step-by-step by assuming a value for the cost price.

Step 1: Define the Cost Price (CP)
Let the cost price of the goods be:

$\mathrm{CP}=100$

Step 2: Calculate the Fixed Price (Marked Price or MP)
Raman fixes the sale price at 16% above the cost price:

$\mathrm{MP}=\mathrm{CP}+(16\%\text{of}\mathrm{CP})$

$\mathrm{MP}=100+16=116$

Step 3: Calculate the Selling Price (SP)
He sells the goods at 12% less than the fixed price (MP):

$\mathrm{SP}=\mathrm{MP}-(12\%\text{of}\mathrm{MP})$

First, find 12% of 116:

$12\%\text{of}116=\frac{12}{100}\times 116=13.92$

Subtract this discount from the marked price to find the selling price:

$\mathrm{SP}=116-13.92=102.08$

Step 4: Calculate the Profit Percentage
Profit is the difference between the Selling Price and the Cost Price:

$\text{Profit}=\mathrm{SP}-\mathrm{CP}$

$\text{Profit}=102.08-100=2.08$

Now, calculate the profit percentage based on the Cost Price:

$\text{Profit Percentage}=\frac{\text{Profit}}{\mathrm{CP}}\times 100\%$

$\text{Profit Percentage}=\frac{2.08}{100}\times 100\%=2.08\%$

Therefore, the profit percentage correct to two places of decimal is 2.08%.