SP of an article is already fixed. If it is sold at `(3)/(4)` th of SP there would be `16(2)/(3)%` loss find the profit % if it is sold at `(6)/(5)` th of S.P.

Answer

To solve the problem step by step, we will break it down as follows:

### Step 1: Define the Selling Price (SP) and Selling Price at Loss
Let the Selling Price (SP) of the article be represented as \( SP = 4x \).

When the article is sold at \( \frac{3}{4} \) of SP, the Selling Price (SP1) becomes:
\[ SP1 = \frac{3}{4} \times SP = \frac{3}{4} \times 4x = 3x \]

### Step 2: Determine the Loss Percentage
According to the problem, selling at \( SP1 \) results in a loss of \( 16 \frac{2}{3} \% \). This can be converted to a fraction:
\[ 16 \frac{2}{3} \% = \frac{50}{3} \% \]
This means the loss is \( \frac{50}{3} \% \) of the Cost Price (CP).

### Step 3: Calculate the Loss in Terms of CP
If we denote the Cost Price as \( CP \), then the loss can be expressed as:
\[ \text{Loss} = \frac{50}{3} \% \text{ of } CP = \frac{50}{300} \times CP = \frac{1}{6} \times CP \]

### Step 4: Relate Selling Price and Cost Price
Since the loss is \( \frac{1}{6} \) of CP, we can express the Selling Price in terms of CP:
\[ SP1 = CP - \text{Loss} = CP - \frac{1}{6}CP = \frac{5}{6}CP \]
From our earlier calculation, we have \( SP1 = 3x \). Therefore:
\[ 3x = \frac{5}{6}CP \]
From this, we can solve for CP:
\[ CP = \frac{3x \times 6}{5} = \frac{18x}{5} \]

### Step 5: Calculate New Selling Price (SP2)
Now, we need to find the profit percentage when the article is sold at \( \frac{6}{5} \) of SP:
\[ SP2 = \frac{6}{5} \times SP = \frac{6}{5} \times 4x = \frac{24x}{5} \]

### Step 6: Calculate Profit
Now we can find the profit:
\[ \text{Profit} = SP2 - CP = \frac{24x}{5} - \frac{18x}{5} = \frac{6x}{5} \]

### Step 7: Calculate Profit Percentage
Profit percentage is given by the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{\frac{6x}{5}}{\frac{18x}{5}} \right) \times 100 = \left( \frac{6}{18} \right) \times 100 = \frac{1}{3} \times 100 = 33 \frac{1}{3} \% \]

### Final Answer
The profit percentage when the article is sold at \( \frac{6}{5} \) of SP is:
\[ \boxed{33 \frac{1}{3} \%} \]