A shop sells an object at a discount of 10% for $180. Find the marked price and the discount of the object.

To find the marked price and the discount amount of the object, we can use the information given:

### Given:
- Selling price after discount (SP) = $180
- Discount percentage = 10%

### Let's find the marked price (MP) first:

The selling price after a discount is given by:

\[
\text{Selling Price (SP)} = \text{Marked Price (MP)} - \text{Discount}
\]

The discount can also be expressed as a percentage of the marked price:

\[
\text{Discount} = \text{Discount Percentage} \times \text{Marked Price (MP)} = \frac{\text{Discount Percentage}}{100} \times \text{MP}
\]

Substituting this into the selling price formula:

\[
\text{SP} = \text{MP} - \frac{\text{Discount Percentage}}{100} \times \text{MP}
\]

\[
\text{SP} = \text{MP} \times \left(1 - \frac{\text{Discount Percentage}}{100}\right)
\]

Now, substitute the values:

\[
180 = \text{MP} \times \left(1 - \frac{10}{100}\right)
\]

\[
180 = \text{MP} \times 0.9
\]

Now, solve for MP:

\[
\text{MP} = \frac{180}{0.9} = 200
\]

### Marked Price (MP) = $200

### Discount:
Now that we have the marked price, we can find the discount:

\[
\text{Discount} = \text{Marked Price (MP)} - \text{Selling Price (SP)} = 200 - 180 = 20
\]

### Discount = $20

### Summary:
- **Marked Price (MP)**: $200
- **Discount**: $20

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

Here are some related questions:
1. If the discount percentage were 15%, what would be the selling price?
2. What would the discount amount be if the marked price was $250 and the discount percentage was 10%?
3. How much would the marked price be if the selling price after a 10% discount was $270?
4. What is the discount percentage if the marked price is $220 and the selling price is $198?
5. How do you calculate the selling price if the marked price and discount percentage are known?

**Tip:** Always double-check whether a percentage is applied to the original (marked) price or another value like the discounted price to avoid confusion in calculations.

Learn how to calculate the marked price and discount percentage of an object using the given selling price after a 10% discount. Get a step-by-step explanation with formulas and examples.

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