A referigerator and a camera were sold for Rs. 12,000 each. The referigerator was sold at a loss of `20%` of the cost and the camera at a gain of `20%` of the cost. The entire transaction results in which one of the following ?

Options

A. No loss or gain
B. Loss of Rs. 1,000
C. Gain of Rs. 1000
D. Loss of Rs. 2,000

Answer

To solve the problem step by step, we will calculate the cost price (CP) of the refrigerator and the camera, determine the total cost price, and then find out if there was a profit or loss in the entire transaction.

### Step 1: Define Variables
Let the cost price of the refrigerator be \( X \) and the cost price of the camera be \( Y \).

### Step 2: Selling Price of Both Items
Both the refrigerator and the camera were sold for Rs. 12,000 each. Therefore, the total selling price (SP) for both items is:
\[ \text{Total SP} = 12,000 + 12,000 = 24,000 \]

### Step 3: Calculate Cost Price of the Refrigerator
The refrigerator was sold at a loss of 20%. The selling price can be expressed as:
\[ \text{SP} = \text{CP} - \text{Loss} \]
Where the loss is 20% of the cost price:
\[ \text{Loss} = 20\% \text{ of } X = \frac{20}{100} \times X = \frac{1}{5}X \]
Thus, we can write:
\[ 12,000 = X - \frac{1}{5}X \]
This simplifies to:
\[ 12,000 = \frac{4}{5}X \]
To find \( X \), we multiply both sides by \( \frac{5}{4} \):
\[ X = 12,000 \times \frac{5}{4} = 15,000 \]

### Step 4: Calculate Cost Price of the Camera
The camera was sold at a gain of 20%. The selling price can be expressed as:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Where the profit is 20% of the cost price:
\[ \text{Profit} = 20\% \text{ of } Y = \frac{20}{100} \times Y = \frac{1}{5}Y \]
Thus, we can write:
\[ 12,000 = Y + \frac{1}{5}Y \]
This simplifies to:
\[ 12,000 = \frac{6}{5}Y \]
To find \( Y \), we multiply both sides by \( \frac{5}{6} \):
\[ Y = 12,000 \times \frac{5}{6} = 10,000 \]

### Step 5: Calculate Total Cost Price
Now, we can find the total cost price of both items:
\[ \text{Total CP} = X + Y = 15,000 + 10,000 = 25,000 \]

### Step 6: Determine Total Profit or Loss
Now we compare the total cost price with the total selling price:
\[ \text{Total SP} = 24,000 \]
\[ \text{Total CP} = 25,000 \]
Since the total cost price is greater than the total selling price, there is a loss:
\[ \text{Loss} = \text{Total CP} - \text{Total SP} = 25,000 - 24,000 = 1,000 \]

### Conclusion
The entire transaction results in a loss of Rs. 1,000.

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