Math Problem Statement

If Purchases were 45% of sales and other expenses were 45% of sales, what would be the increase in profit if, through better purchasing, the cost of purchases was reduced to 43% of sales?

Solution

To calculate the increase in profit, we need to compare the initial situation (with purchases at 45% of sales) and the new situation (with purchases reduced to 43% of sales). Here’s the breakdown of the problem:

Initial Situation:

  • Purchases = 45% of sales
  • Other expenses = 45% of sales
  • Total costs = Purchases + Other expenses = 45% + 45% = 90% of sales
  • Profit (before the reduction) = Sales - Total costs = 100% - 90% = 10% of sales

New Situation:

  • Purchases are now reduced to 43% of sales
  • Other expenses remain 45% of sales
  • New total costs = 43% + 45% = 88% of sales
  • New profit = 100% - 88% = 12% of sales

Increase in Profit:

The initial profit was 10% of sales, and the new profit is 12% of sales. Therefore, the increase in profit is:

Increase in profit=12%10%=2% of sales\text{Increase in profit} = 12\% - 10\% = 2\% \text{ of sales}

So, the profit will increase by 2% of sales due to the reduction in purchase costs.

Would you like more details on this calculation or further clarification?

Here are some related questions:

  1. How does a decrease in expenses impact the profit margin?
  2. What other strategies could further increase profit margins?
  3. How do fixed and variable costs differ in their impact on profit?
  4. How could this same approach apply to managing "other expenses"?
  5. What is the importance of understanding percentage changes in business financials?

Tip: Always track and analyze your expense percentages regularly to find areas where cost-saving measures can improve profitability.

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Math Problem Analysis

Mathematical Concepts

Percentage Calculation
Profit Margin
Cost Reduction

Formulas

Profit = Sales - (Purchases + Other Expenses)
Increase in Profit = New Profit - Old Profit

Theorems

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Suitable Grade Level

Grades 9-11