The CP of an aritcle is 5/6 th of the SP. What is the percentage profit or loss?

Options

A. 20% loss
B. 16.66% profit
C. 16.66% loss
D. 20% profit

Answer

To solve the problem, we need to find the percentage profit or loss given that the cost price (CP) of an article is \( \frac{5}{6} \) of the selling price (SP).

### Step-by-Step Solution:

1. **Understand the relationship between CP and SP**:
We know that:
\[ CP = \frac{5}{6} \times SP \]

2. **Express SP in terms of CP**:
To express SP in terms of CP, we can rearrange the equation:
\[ SP = \frac{6}{5} \times CP \]

3. **Calculate the profit**:
Profit is calculated as:
\[ Profit = SP - CP \]
Substituting the expression for SP:
\[ Profit = \left(\frac{6}{5} \times CP\right) - CP \]
To combine the terms, we can express CP as \( \frac{5}{5} \times CP \):
\[ Profit = \left(\frac{6}{5} \times CP - \frac{5}{5} \times CP\right) = \frac{1}{5} \times CP \]

4. **Calculate the profit percentage**:
The profit percentage is given by the formula:
\[ \text{Profit Percentage} = \left(\frac{Profit}{CP}\right) \times 100 \]
Substituting the value of Profit:
\[ \text{Profit Percentage} = \left(\frac{\frac{1}{5} \times CP}{CP}\right) \times 100 \]
Simplifying this gives:
\[ \text{Profit Percentage} = \left(\frac{1}{5}\right) \times 100 = 20\% \]

### Final Answer:
The percentage profit is **20%**.

---