Solving for the Cost Price

Oct 13, 2025 by miodeya.com 136 views

Introduction

In the world of mathematics, problems often arise from everyday situations, and solving them requires a combination of logical thinking and mathematical skills. In this article, we will delve into a problem that involves finding the cost price of a chair, given that it was sold for a certain amount and resulted in a loss of 15%. Our goal is to uncover the cost price of the chair, and we will use mathematical concepts to achieve this.

Understanding the Problem

Ali sells a chair for *1564, and in doing so, he suffers a loss of 15%. This means that the selling price of the chair is 85% of its cost price, as the loss is 15% of the cost price. We need to find the cost price of the chair, which is the original price at which Ali purchased the chair.

Breaking Down the Problem

To solve this problem, we can use the concept of percentages. We know that the selling price of the chair is *1564, and this is 85% of the cost price. We can represent this as an equation:

Selling Price = 85% of Cost Price

We can convert the percentage to a decimal by dividing by 100:

Selling Price = 0.85 x Cost Price

Solving for the Cost Price

Now that we have the equation, we can solve for the cost price. We know that the selling price is *1564, so we can substitute this value into the equation:

1564 = 0.85 x Cost Price

To find the cost price, we can divide both sides of the equation by 0.85:

Cost Price = 1564 ÷ 0.85

Calculating the Cost Price

Now that we have the equation, we can calculate the cost price:

Cost Price = 1564 ÷ 0.85 Cost Price = 1835.29

Rounding the Answer

Since we are dealing with money, we can round the answer to the nearest whole number. In this case, we can round 1835.29 to 1835.

Conclusion

In this article, we have solved a problem that involves finding the cost price of a chair, given that it was sold for a certain amount and resulted in a loss of 15%. We used mathematical concepts, such as percentages and decimals, to achieve this. By following the steps outlined in this article, we were able to find the cost price of the chair, which is 1835.

Additional Examples

Here are a few additional examples of how to use the concept of percentages to solve problems:

If a shirt is sold for *1200, and the selling price is 90% of the cost price, what is the cost price of the shirt?
If a book is sold for *15, and the selling price is 80% of the cost price, what is the cost price of the book?

Tips and Tricks

Here are a few tips and tricks to help you solve problems involving percentages:

Always convert percentages to decimals by dividing by 100.
Use the concept of percentages to set up equations and solve for unknown values.
Be careful when rounding answers, as small errors can add up quickly.

Final Thoughts

Introduction

In our previous article, we explored the concept of percentages and how to use them to solve problems. We also provided a step-by-step guide on how to find the cost price of a chair, given that it was sold for a certain amount and resulted in a loss of 15%. In this article, we will answer some frequently asked questions related to solving problems involving percentages.

Q: What is the difference between a percentage and a decimal?

A: A percentage is a way of expressing a value as a fraction of 100. For example, 25% is equal to 0.25. A decimal, on the other hand, is a way of expressing a value as a fraction of 10. For example, 0.25 is equal to 25%.

Q: How do I convert a percentage to a decimal?

A: To convert a percentage to a decimal, simply divide the percentage by 100. For example, to convert 25% to a decimal, you would divide 25 by 100, which equals 0.25.

Q: How do I convert a decimal to a percentage?

A: To convert a decimal to a percentage, simply multiply the decimal by 100. For example, to convert 0.25 to a percentage, you would multiply 0.25 by 100, which equals 25%.

Q: What is the formula for finding the cost price of an item?

A: The formula for finding the cost price of an item is:

Cost Price = Selling Price ÷ (1 - Loss Percentage)

For example, if an item is sold for $100 and the loss percentage is 20%, the cost price would be:

Cost Price = $100 ÷ (1 - 0.20) Cost Price = $100 ÷ 0.80 Cost Price = $125

Q: How do I find the selling price of an item if I know the cost price and the loss percentage?

A: To find the selling price of an item, you can use the following formula:

Selling Price = Cost Price x (1 - Loss Percentage)

For example, if the cost price of an item is $100 and the loss percentage is 20%, the selling price would be:

Selling Price = $100 x (1 - 0.20) Selling Price = $100 x 0.80 Selling Price = $80

Q: What is the difference between a discount and a loss?

A: A discount is a reduction in the price of an item, whereas a loss is a reduction in the value of an item. For example, if an item is sold for $100 and the discount is 20%, the selling price would be $80. However, if the item is sold for $80 and the loss is 20%, the cost price would be $100.

Q: How do I calculate the discount on an item?

A: To calculate the discount on an item, you can use the following formula:

Discount = (Original Price - Selling Price) / Original Price

For example, if the original price of an item is $100 and the selling price is $80, the discount would be:

Discount = ($100 - $80) / $100 Discount = $20 / $100 Discount = 0.20 or 20%

Q: How do I calculate the loss on an item?

A: To calculate the loss on an item, you can use the following formula:

Loss = (Cost Price - Selling Price) / Cost Price

For example, if the cost price of an item is $100 and the selling price is $80, the loss would be:

Loss = ($100 - $80) / $100 Loss = $20 / $100 Loss = 0.20 or 20%

Conclusion

In this article, we have answered some frequently asked questions related to solving problems involving percentages. We hope that this article has provided you with a better understanding of how to use percentages to solve problems and has helped you to develop your problem-solving skills.