Peter sold two phones for $9999 each. He lost 10% on one and gained 10% on the other. After two transactions, find the overall profit or loss that he had.

Steps to Solve

1. Calculate the loss on the first phone

The first phone was sold at a loss of 10%. To find the loss amount:

Loss = Selling Price × Loss Percentage
$$ \text{Loss} = 9999 \times 0.10 = 999.9 $$

Now, subtract the loss from the selling price to find the cost price:

Cost Price = Selling Price - Loss
$$ \text{Cost Price} = 9999 - 999.9 = 8999.1 $$

2. Calculate the gain on the second phone

The second phone was sold at a gain of 10%. To find the gain amount:

Gain = Selling Price × Gain Percentage
$$ \text{Gain} = 9999 \times 0.10 = 999.9 $$

Now, add the gain to the selling price to find the cost price:

Cost Price = Selling Price + Gain
$$ \text{Cost Price} = 9999 + 999.9 = 10998.9 $$

3. Calculate the overall profit or loss

Now, we find the total cost price and total selling price:

Total Selling Price = Selling Price of Phone 1 + Selling Price of Phone 2
$$ \text{Total Selling Price} = 9999 + 9999 = 19998 $$

Total Cost Price = Cost Price of Phone 1 + Cost Price of Phone 2
$$ \text{Total Cost Price} = 8999.1 + 10998.9 = 19998 $$

Now, calculate the overall profit or loss:

Overall Profit/Loss = Total Selling Price - Total Cost Price
$$ \text{Overall Profit/Loss} = 19998 - 19998 = 0 $$

4. Conclusion

The overall profit or loss after these transactions is zero.