If selling price of an article `(8)/(5)` is times its cost price, the profit percent on it is

Answer

To solve the problem, we need to find the profit percentage when the selling price (SP) of an article is \( \frac{8}{5} \) times its cost price (CP).

### Step-by-step Solution:

1. **Define the Cost Price (CP)**:
Let the cost price (CP) of the article be \( x \).

2. **Calculate the Selling Price (SP)**:
According to the problem, the selling price (SP) is given as:
\[ SP = \frac{8}{5} \times CP = \frac{8}{5} \times x = \frac{8x}{5} \]

3. **Calculate the Profit**:
Profit can be calculated using the formula:
\[ \text{Profit} = SP - CP \]
Substituting the values we have:
\[ \text{Profit} = \frac{8x}{5} - x \]
To subtract \( x \), we convert \( x \) into a fraction with a common denominator:
\[ x = \frac{5x}{5} \]
Now substituting back:
\[ \text{Profit} = \frac{8x}{5} - \frac{5x}{5} = \frac{8x - 5x}{5} = \frac{3x}{5} \]

4. **Calculate the Profit Percentage**:
Profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left( \frac{\frac{3x}{5}}{x} \right) \times 100 \]
Simplifying this gives:
\[ \text{Profit Percentage} = \left( \frac{3}{5} \right) \times 100 = 60\% \]

### Final Answer:
The profit percentage on the article is **60%**.