A shopkeeper sold a sewing machine for Rs 1,080 at a loss of 10%. At what price should he have sold it so as to gain 10% on it ? (in Rs )
एक दुकानदार ने एक सिलाई मशीन 10% की हानि पर Rs 1,080 में बेची। उसे वह किस कीमत में बेचता तो उसे 10% का लाभ होता?

Options

A. A)1069
B. B)1200
C. C)1230
D. D)1320

Explanation

To solve the problem step by step, we will first determine the cost price (CP) of the sewing machine based on the given selling price (SP) and loss percentage. Then, we will find out the selling price required to achieve a gain of 10%.

### Step 1: Understand the given information
- Selling Price (SP) at a loss of 10% = Rs 1,080
- Loss Percentage = 10%

### Step 2: Calculate the Cost Price (CP)
When there is a loss of 10%, the Selling Price is 90% of the Cost Price. We can express this relationship mathematically:
\[ SP = CP \times \left(1 - \frac{\text{Loss \%}}{100}\right) \]
Substituting the values:
\[ 1080 = CP \times \left(1 - \frac{10}{100}\right) \]
\[ 1080 = CP \times 0.90 \]

### Step 3: Solve for CP
To find CP, we rearrange the equation:
\[ CP = \frac{1080}{0.90} \]
Calculating this gives:
\[ CP = 1200 \]

### Step 4: Calculate the Selling Price for a 10% Gain
To find the Selling Price (SP) for a gain of 10%, we use the formula:
\[ SP = CP \times \left(1 + \frac{\text{Gain \%}}{100}\right) \]
Substituting the values:
\[ SP = 1200 \times \left(1 + \frac{10}{100}\right) \]
\[ SP = 1200 \times 1.10 \]

### Step 5: Solve for SP
Calculating this gives:
\[ SP = 1320 \]

### Final Answer
The price at which the shopkeeper should have sold the sewing machine to gain 10% is **Rs 1,320**.

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