Calculating Cost Price from Loss

The shopkeeper sells an article for ₹31, incurring a 7% loss. We can find the Cost Price (CP) using the formula:

$SP = CP \times (1 - \frac{Loss\%}{100})$

Substituting the values:

$31 = CP \times (1 - \frac{7}{100})$

$31 = CP \times (1 - 0.07)$

$31 = CP \times 0.93$

Now, solve for CP:

$CP = \frac{31}{0.93}$

Calculating Profit Percentage

The shopkeeper wants to sell the same article for ₹35. We need to find the profit percentage.

First, calculate the profit amount:

$Profit = New SP - CP$

$Profit = 35 - \frac{31}{0.93}$

To make calculation easier, let's find the profit using the formula directly involving SPs and percentages:

$Profit\% = (\frac{New SP - CP}{CP}) \times 100$

$Profit\% = (\frac{35 - \frac{31}{0.93}}{\frac{31}{0.93}}) \times 100$

Simplify the expression:

$Profit\% = (\frac{35 \times 0.93 - 31}{31}) \times 100$

$Profit\% = (\frac{32.55 - 31}{31}) \times 100$

$Profit\% = (\frac{1.55}{31}) \times 100$

$Profit\% = 0.05 \times 100$

$Profit\% = 5\%$

Final Answer

When the shopkeeper sells the article for ₹35, the profit percentage is 5%.