A person sold two steel almirahs for Rs. `1980` each. On one he gained `10%` while on the other he lost `10%` . In the bargain he

Options

A. Neither gained nor lost
B. Gained `1%`
C. Lost `1%`
D. Gained `2%`

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Selling Prices
The person sold two steel almirahs for Rs. 1980 each. Therefore, the selling price (SP) for each almirah is:
- SP1 = Rs. 1980 (for the first almirah with a gain of 10%)
- SP2 = Rs. 1980 (for the second almirah with a loss of 10%)

### Step 2: Calculate the Cost Price for Each Almirah
1. **For the first almirah (10% gain)**:
- Let the cost price (CP1) be \( x \).
- Since there is a gain of 10%, we can express the selling price as:
\[ SP1 = CP1 + 10\% \text{ of } CP1 = CP1 \times \left(1 + \frac{10}{100}\right) = CP1 \times 1.1 \]
- Setting this equal to the selling price:
\[ 1980 = x \times 1.1 \]
- Solving for \( x \):
\[ x = \frac{1980}{1.1} = 1800 \]
- Therefore, the cost price of the first almirah (CP1) is Rs. 1800.

2. **For the second almirah (10% loss)**:
- Let the cost price (CP2) be \( y \).
- Since there is a loss of 10%, we can express the selling price as:
\[ SP2 = CP2 - 10\% \text{ of } CP2 = CP2 \times \left(1 - \frac{10}{100}\right) = CP2 \times 0.9 \]
- Setting this equal to the selling price:
\[ 1980 = y \times 0.9 \]
- Solving for \( y \):
\[ y = \frac{1980}{0.9} = 2200 \]
- Therefore, the cost price of the second almirah (CP2) is Rs. 2200.

### Step 3: Calculate Total Cost Price and Total Selling Price
- Total Cost Price (CP) = CP1 + CP2
\[ CP = 1800 + 2200 = 4000 \]
- Total Selling Price (SP) = SP1 + SP2
\[ SP = 1980 + 1980 = 3960 \]

### Step 4: Determine Overall Gain or Loss
- To find the overall gain or loss, we subtract the total cost price from the total selling price:
\[ \text{Loss} = CP - SP = 4000 - 3960 = 40 \]
- To find the percentage loss:
\[ \text{Percentage Loss} = \left(\frac{\text{Loss}}{\text{Total CP}}\right) \times 100 = \left(\frac{40}{4000}\right) \times 100 = 1\% \]

### Conclusion
The person incurred a loss of 1%. Therefore, the answer is:
**C) lost 1%**