The marked price of an article is 10/7 of the cost price and the selling price of that article is 4/5 of the marked price. What is the profit percentage?

Options

A. `17.24`
B. `16.66`
C. `14.28`
D. `15.42`

Answer

To find the profit percentage based on the given information, we can follow these steps:

### Step 1: Define the Cost Price (CP)
Let the Cost Price (CP) of the article be denoted as \( CP \).

### Step 2: Calculate the Marked Price (MP)
According to the problem, the marked price (MP) is given as:
\[ MP = \frac{10}{7} \times CP \]

### Step 3: Calculate the Selling Price (SP)
The selling price (SP) is given as:
\[ SP = \frac{4}{5} \times MP \]
Substituting the value of MP from Step 2:
\[ SP = \frac{4}{5} \times \left(\frac{10}{7} \times CP\right) \]

### Step 4: Simplify the Selling Price (SP)
Now, we can simplify the expression for SP:
\[ SP = \frac{4 \times 10}{5 \times 7} \times CP = \frac{40}{35} \times CP = \frac{8}{7} \times CP \]

### Step 5: Calculate the Profit
Profit is calculated as:
\[ \text{Profit} = SP - CP \]
Substituting the value of SP:
\[ \text{Profit} = \left(\frac{8}{7} \times CP\right) - CP \]
To combine the terms, express CP as \(\frac{7}{7} \times CP\):
\[ \text{Profit} = \left(\frac{8}{7} - \frac{7}{7}\right) \times CP = \frac{1}{7} \times CP \]

### Step 6: Calculate the Profit Percentage
The profit percentage is given by the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{CP}\right) \times 100 \]
Substituting the profit value:
\[ \text{Profit Percentage} = \left(\frac{\frac{1}{7} \times CP}{CP}\right) \times 100 = \frac{1}{7} \times 100 \]
Calculating this gives:
\[ \text{Profit Percentage} = \frac{100}{7} \approx 14.2857 \approx 14.29\% \]

### Conclusion
Thus, the profit percentage is approximately 14.29%.

### Final Answer
The closest option is **C: 14.28%**.

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