On selling an article for ₹ 576 a trader loses `4%`. In order to gain `4(1)/6%`, he must sell that article for:

Options

A. ₹ 636
B. ₹ 676
C. ₹ 625
D. can't be determined

Answer

To solve the problem step by step, we will follow the given information and apply the concepts of profit, loss, and percentage calculations.

### Step 1: Understand the Selling Price and Loss
We know that the selling price (SP) of the article is ₹576 and the trader incurs a loss of 4%.

**Hint:** Remember that a loss percentage means the selling price is less than the cost price.

### Step 2: Calculate the Cost Price (CP)
Since there is a 4% loss, the selling price is 96% of the cost price (CP). We can express this relationship mathematically as:
\[ SP = CP \times \left(1 - \frac{Loss\%}{100}\right) \]
Substituting the values we have:
\[ 576 = CP \times \left(1 - \frac{4}{100}\right) \]
\[ 576 = CP \times 0.96 \]

**Hint:** To find CP, you need to isolate it on one side of the equation.

### Step 3: Solve for CP
Now, we can rearrange the equation to find CP:
\[ CP = \frac{576}{0.96} \]
Calculating this gives:
\[ CP = 600 \]

**Hint:** When dividing, ensure you perform the division accurately to avoid mistakes.

### Step 4: Determine the Desired Profit Percentage
Next, we need to find the selling price that would give a profit of \(4\frac{1}{6}\%\). This can be converted to an improper fraction:
\[ 4\frac{1}{6}\% = \frac{25}{6}\% \]

**Hint:** Converting mixed numbers to improper fractions can simplify calculations.

### Step 5: Calculate the New Selling Price for Desired Profit
To find the new selling price (SP') that gives a profit of \(\frac{25}{6}\%\), we use the formula:
\[ SP' = CP \times \left(1 + \frac{Profit\%}{100}\right) \]
Substituting the values:
\[ SP' = 600 \times \left(1 + \frac{25}{6 \times 100}\right) \]
Calculating the profit percentage:
\[ SP' = 600 \times \left(1 + \frac{25}{600}\right) \]
\[ SP' = 600 \times \left(1 + 0.04167\right) \]
\[ SP' = 600 \times 1.04167 \]

**Hint:** Make sure to add the profit percentage correctly to 1.

### Step 6: Final Calculation
Now, calculating the final selling price:
\[ SP' = 600 \times 1.04167 \approx 625 \]

**Hint:** Rounding off the final answer is important to match the context of the problem.

### Conclusion
Thus, the trader must sell the article for **₹625** to achieve the desired profit of \(4\frac{1}{6}\%\).