A shop sells an object for $162 with a profit of 8%. Find the cost and profit.

To find the cost price and the profit amount of the object, we can use the information given:

### Given:
- Selling price (SP) = $162
- Profit percentage = 8%

### Let's find the cost price (CP) first:

The formula for selling price in terms of cost price and profit percentage is:

\[
\text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit}
\]

But profit can also be expressed as a percentage of the cost price:

\[
\text{Profit} = \text{Profit Percentage} \times \text{Cost Price (CP)} = \frac{\text{Profit Percentage}}{100} \times \text{CP}
\]

Substitute this into the selling price formula:

\[
\text{SP} = \text{CP} + \frac{\text{Profit Percentage}}{100} \times \text{CP}
\]

\[
\text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right)
\]

Now, substitute the values:

\[
162 = \text{CP} \times \left(1 + \frac{8}{100}\right)
\]

\[
162 = \text{CP} \times 1.08
\]

Now, solve for CP:

\[
\text{CP} = \frac{162}{1.08} = 150
\]

### Cost Price (CP) = $150

### Profit:
Now that we have the cost price, we can find the profit:

\[
\text{Profit} = \text{SP} - \text{CP} = 162 - 150 = 12
\]

### Profit = $12

### Summary:
- **Cost Price (CP)**: $150
- **Profit**: $12

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

Here are some related questions:
1. If the profit percentage were 10%, what would be the cost price?
2. What would the selling price be if the profit percentage was increased to 12%?
3. How much would the cost price be if the selling price was $180 with the same 8% profit?
4. What is the percentage profit if the cost price is $140 and the selling price is $162?
5. How do you calculate the profit percentage if the cost and selling prices are known?

**Tip:** When solving profit and cost-related problems, always ensure that you correctly identify whether the profit percentage is based on the cost price or the selling price.

Learn how to calculate the cost price and profit when an object is sold for $162 with an 8% profit margin. Understand the formulas for profit and profit percentage calculations. Suitable for high school students studying profit and loss problems.

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