By selling cloth at Rs. 9 per metre, a shopkeeper loses 10%. Find the rate at which it should be sold so as to earn profit of 15%.

Options

A. Rs. 11.20
B. Rs. 11.30
C. Rs. 11.40
D. Rs. 11.50

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the Cost Price (CP)
Given that the shopkeeper sells cloth at Rs. 9 per meter and incurs a loss of 10%, we can find the cost price (CP) using the formula for loss:

\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} \times \left(1 - \frac{\text{Loss \%}}{100}\right) \]

Here, the loss percentage is 10%, and the selling price is Rs. 9.

### Step 2: Substitute the values into the formula
Substituting the known values into the formula:

\[ 9 = CP \times \left(1 - \frac{10}{100}\right) \]

This simplifies to:

\[ 9 = CP \times 0.9 \]

### Step 3: Solve for Cost Price (CP)
Now, we can solve for CP:

\[ CP = \frac{9}{0.9} = 10 \text{ Rs.} \]

### Step 4: Calculate the Selling Price for 15% Profit
To find the selling price (SP) that would give a profit of 15%, we use the formula for profit:

\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} \times \left(1 + \frac{\text{Profit \%}}{100}\right) \]

Substituting the cost price and the profit percentage:

\[ SP = 10 \times \left(1 + \frac{15}{100}\right) \]

### Step 5: Simplify the Selling Price Calculation
This simplifies to:

\[ SP = 10 \times 1.15 = 11.5 \text{ Rs.} \]

### Conclusion
Thus, the rate at which the shopkeeper should sell the cloth to earn a profit of 15% is Rs. 11.50 per meter.

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