A dealer sold two coolers at 2,970 cach. On selling one cooler, he gained 10%, on selling the other he lost 10%. Find the dealer's gain or loss per cent.

Options

A. 1%loss
B. 1%gain
C. 2%loss
D. 2%gain

Answer

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

### Step 1: Understand the Selling Prices
The dealer sold two coolers for a total of 2,970 each. Thus, the selling price (SP) of each cooler is:
\[ SP_1 = SP_2 = 2970 \]

### Step 2: Calculate the Cost Price of Each Cooler
Let the cost price (CP) of the first cooler be \( CP_1 \) and the second cooler be \( CP_2 \).

For the first cooler, the dealer gains 10%. Therefore, we can express the selling price in terms of the cost price:
\[ SP_1 = CP_1 + 10\% \text{ of } CP_1 \]
This can be rewritten as:
\[ SP_1 = CP_1 + 0.1 \times CP_1 = 1.1 \times CP_1 \]
From this, we can find \( CP_1 \):
\[ CP_1 = \frac{SP_1}{1.1} = \frac{2970}{1.1} = 2700 \]

For the second cooler, the dealer incurs a loss of 10%. Thus, we can express the selling price as:
\[ SP_2 = CP_2 - 10\% \text{ of } CP_2 \]
This can be rewritten as:
\[ SP_2 = CP_2 - 0.1 \times CP_2 = 0.9 \times CP_2 \]
From this, we can find \( CP_2 \):
\[ CP_2 = \frac{SP_2}{0.9} = \frac{2970}{0.9} = 3300 \]

### Step 3: Calculate Total Cost Price and Total Selling Price
Now, we can find the total cost price (CP) and total selling price (SP) of both coolers:
\[ \text{Total CP} = CP_1 + CP_2 = 2700 + 3300 = 6000 \]
\[ \text{Total SP} = SP_1 + SP_2 = 2970 + 2970 = 5940 \]

### Step 4: Calculate Overall Gain or Loss
To find the overall gain or loss, we subtract the total cost price from the total selling price:
\[ \text{Loss} = \text{Total CP} - \text{Total SP} = 6000 - 5940 = 60 \]

### Step 5: Calculate Loss Percentage
Finally, we can calculate the loss percentage using the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Total CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Loss Percentage} = \left( \frac{60}{6000} \right) \times 100 = 1\% \]

### Final Answer
The dealer's overall loss percentage is **1%**.

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