Understanding Company Profit and Income Ratio

This problem involves analyzing data from a table showing the percentage profit earned by two companies, ABC and XYZ, over several years. We are specifically asked to find the ratio of their total incomes in the year 2015, given that their investments in that year were equal.

Analyzing the Given Data Table

Let's look at the relevant data for the year 2015 from the provided table:

From the table, for the year 2015:

• Percentage Profit for Company ABC = 60%
• Percentage Profit for Company XYZ = 50%

Relating Profit, Investment, and Income

The percentage profit is calculated based on the investment. The formula for percentage profit is:

\(\text{Percentage Profit} = \frac{\text{Profit}}{\text{Investment}} \times 100\)

Total income of a company is the sum of its investment and the profit earned:

\(\text{Income} = \text{Investment} + \text{Profit}\)

We can also express Income in terms of Investment and Percentage Profit. From the profit formula, we get:

\(\text{Profit} = \frac{\text{Percentage Profit}}{100} \times \text{Investment}\)

Substituting this into the Income formula:

\(\text{Income} = \text{Investment} + \left(\frac{\text{Percentage Profit}}{100} \times \text{Investment}\right)\)

\(\text{Income} = \text{Investment} \times \left(1 + \frac{\text{Percentage Profit}}{100}\right)\)

Calculating Income for ABC and XYZ in 2015

We are given that the amounts invested by the two companies in 2015 were equal. Let's assume the investment for both companies in 2015 was \(I\).

For Company ABC in 2015:

• Investment = \(I\)
• Percentage Profit = 60%
• Income (\(Income_{\text{ABC}}\)) = \(I \times \left(1 + \frac{60}{100}\right) = I \times \left(1 + 0.6\right) = I \times 1.6\)

For Company XYZ in 2015:

• Investment = \(I\)
• Percentage Profit = 50%
• Income (\(Income_{\text{XYZ}}\)) = \(I \times \left(1 + \frac{50}{100}\right) = I \times \left(1 + 0.5\right) = I \times 1.5\)

Finding the Ratio of Total Income

We need to find the ratio of the total income of company ABC to that of company XYZ in 2015. This ratio is:

\(\text{Ratio} = \frac{Income_{\text{ABC}}}{Income_{\text{XYZ}}}\)

Substitute the calculated income values:

\(\text{Ratio} = \frac{I \times 1.6}{I \times 1.5}\)

Since \(I\) is the same for both and \(I \neq 0\), we can cancel \(I\):

\(\text{Ratio} = \frac{1.6}{1.5}\)

To express this as a ratio of integers, we can multiply the numerator and denominator by 10:

\(\text{Ratio} = \frac{1.6 \times 10}{1.5 \times 10} = \frac{16}{15}\)

So, the ratio of the total income of company ABC to that of company XYZ in 2015 is 16 : 15.

Conclusion

Given that the investments were equal in 2015, and the profit percentages were 60% for ABC and 50% for XYZ, the ratio of their total incomes is calculated as 16 : 15.

Revision Table: Profit, Investment, and Income

Additional Information: Data Interpretation Tips

When solving data interpretation problems involving tables like this, keep the following tips in mind:

• Always carefully read the question and understand exactly what is being asked (e.g., ratio of income, difference in profit, average profit).
• Identify the specific data points needed from the table based on the years and companies mentioned in the question.
• Pay close attention to the units or type of data (e.g., percentage profit, absolute values).
• Understand the relationship between different financial terms like Investment, Profit, Income, Expenditure, etc.
• Use the correct formulas for calculating percentages, ratios, averages, etc.
• When comparing values or calculating ratios, ensure you are using the correct base values (e.g., percentage profit is on investment, not income).
• Break down complex problems into smaller steps.
• Double-check your calculations, especially when dealing with percentages and decimals.
• Be mindful of any specific conditions given in the question, such as "investments were equal" as in this problem.