If selling price of an article is $\frac{7}{6}$ of its cost price. Then the profit percentage in the transaction is:

$16\frac{2}{3}\%$

The correct answer is Option (3) → $16\frac{2}{3}\%$

1. Identify the Relationship

The problem states that the Selling Price ($SP$) is $\frac{7}{6}$ of the Cost Price ($CP$).

Mathematically, this is:

$SP = \frac{7}{6} \times CP$

Alternatively, we can express the ratio as:

$\frac{SP}{CP} = \frac{7}{6}$

This means if the Cost Price is 6, the Selling Price is 7.

2. Calculate the Profit

Profit is the difference between the Selling Price and the Cost Price:

$\text{Profit} = SP - CP$

$\text{Profit} = 7 - 6 = 1 \text{ unit}$

3. Calculate the Profit Percentage

The formula for profit percentage is:

$\text{Profit}\% = \left( \frac{\text{Profit}}{CP} \right) \times 100$

Substitute the values:

$\text{Profit}\% = \left( \frac{1}{6} \right) \times 100$

$\text{Profit}\% = \frac{100}{6} = \frac{50}{3}$

To convert this into a mixed fraction:

$\frac{50}{3} = 16 \frac{2}{3}\%$