A trader sells an item for $1550 at a loss of 18%. What was the cost price of the item?

$1980

$1890

$2198

O $2153

To find the cost price of the item, we use the formula for loss:

\[
\text{Loss Percentage} = \left( \frac{\text{Cost Price} - \text{Selling Price}}{\text{Cost Price}} \right) \times 100
\]

We are given:
- Selling Price (S.P.) = $1550
- Loss Percentage = 18%

The formula for selling price when there is a loss is:

\[
\text{Selling Price} = \text{Cost Price} \times \left( 1 - \frac{\text{Loss Percentage}}{100} \right)
\]

Substituting the values:

\[
1550 = \text{Cost Price} \times \left( 1 - \frac{18}{100} \right)
\]

\[
1550 = \text{Cost Price} \times 0.82
\]

To find the cost price (C.P.), divide both sides by 0.82:

\[
\text{Cost Price} = \frac{1550}{0.82} = 1890.24
\]

Therefore, the closest answer is **$1890**.

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Would you like more details or have any questions about this solution?

Here are 5 related questions:
1. How would the calculation change if the loss percentage was 12%?
2. What if the trader made a profit of 18% instead of a loss?
3. How would you calculate the profit or loss if only the cost price and selling price were known?
4. How is loss percentage different from markup percentage?
5. What is the formula for calculating the cost price when the selling price and profit percentage are known?

**Tip:** Always double-check if the percentage is for profit or loss, as it changes the formula!

A trader sells an item for $1550 at a loss of 18%. What was the cost price of the item?

Learn how to calculate the cost price when a trader sells an item for $1550 at a loss of 18%. This problem involves key concepts like percentages and the formula for calculating loss in commercial arithmetic. Suitable for students in Grades 6-8.

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