A television and a washing machine were sold for 12500 each. If the television was sold at a gain of 30% and the washing machine at a loss of 30%, then the entire transaction resulted in

Options

A. 9% gain
B. 9% loss
C. 11% gain
D. Neither gain nor loss

Answer

To solve the problem, we need to find out the cost price of the television and the washing machine, and then determine the overall gain or loss from the entire transaction.

### Step 1: Calculate the Cost Price of the Television
Let the cost price of the television be \( CP_{TV} \).

Given that the television was sold at a gain of 30%, we can use the formula for selling price:
\[ SP = CP + \text{Gain} \]
Where Gain = \( 30\% \) of \( CP_{TV} \).

The selling price of the television is given as \( 12,500 \):
\[ 12,500 = CP_{TV} + 0.30 \times CP_{TV} \]
\[ 12,500 = 1.30 \times CP_{TV} \]

Now, we can solve for \( CP_{TV} \):
\[ CP_{TV} = \frac{12,500}{1.30} = 9,615.38 \text{ (approximately)} \]

### Step 2: Calculate the Cost Price of the Washing Machine
Let the cost price of the washing machine be \( CP_{WM} \).

Given that the washing machine was sold at a loss of 30%, we can use the formula for selling price:
\[ SP = CP - \text{Loss} \]
Where Loss = \( 30\% \) of \( CP_{WM} \).

The selling price of the washing machine is also \( 12,500 \):
\[ 12,500 = CP_{WM} - 0.30 \times CP_{WM} \]
\[ 12,500 = 0.70 \times CP_{WM} \]

Now, we can solve for \( CP_{WM} \):
\[ CP_{WM} = \frac{12,500}{0.70} = 17,857.14 \text{ (approximately)} \]

### Step 3: Calculate the Total Cost Price and Total Selling Price
Now, we can calculate the total cost price and total selling price:
\[ \text{Total Cost Price} = CP_{TV} + CP_{WM} = 9,615.38 + 17,857.14 = 27,472.52 \]
\[ \text{Total Selling Price} = 12,500 + 12,500 = 25,000 \]

### Step 4: Calculate the Overall Gain or Loss
Now we can find out whether there was a gain or loss:
\[ \text{Overall Gain/Loss} = \text{Total Selling Price} - \text{Total Cost Price} \]
\[ \text{Overall Gain/Loss} = 25,000 - 27,472.52 = -2,472.52 \]

Since the result is negative, it indicates a loss.

### Conclusion
The entire transaction resulted in a loss of approximately \( 2,472.52 \).

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