Understanding Profit Percentage and Income Calculation

This question requires us to analyze data from the provided table showing the percentage profit earned by two companies, ABC and XYZ, over several years. We need to use the given information about company ABC's investment and the relationship between its income in 2013 and 2015 to find the income in 2015.

The table provides the following data:

Analyzing the Given Information for Company ABC

We are given the following specific details about company ABC:

• The income of company ABC in 2013 and that in 2015 were equal.
• The amount invested by company ABC in 2013 was Rs. 8,00,000.

From the table, we find the percentage profit for company ABC in the relevant years:

• Percent profit earned by company ABC in 2013 = 50%
• Percent profit earned by company ABC in 2015 = 60%

Calculating Income based on Profit Percentage

The formula for calculating percentage profit is:

Percentage Profit $= \frac{\text{Income} - \text{Investment}}{\text{Investment}} \times 100$

This formula can be rearranged to find the relationship between Income, Investment, and Profit Percentage:

$\text{Income} - \text{Investment} = \frac{\text{Percentage Profit}}{100} \times \text{Investment}$

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

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

Step-by-Step Calculation of Income in 2013

We know the investment and profit percentage for company ABC in 2013. We can use the formula to calculate the income in 2013.

• Investment in 2013 = Rs. 8,00,000
• Percentage Profit in 2013 = 50%

Using the formula:

Income in 2013 $= \text{Investment in 2013} \times \left( 1 + \frac{\text{Percentage Profit in 2013}}{100} \right)$

Income in 2013 $= 8,00,000 \times \left( 1 + \frac{50}{100} \right)$

Income in 2013 $= 8,00,000 \times \left( 1 + 0.50 \right)$

Income in 2013 $= 8,00,000 \times 1.50$

Income in 2013 $= 12,00,000$

So, the income of company ABC in 2013 was Rs. 12,00,000.

Determining Income in 2015

The question states that the income of company ABC in 2013 and that in 2015 were equal.

Income in 2015 = Income in 2013

Since Income in 2013 is Rs. 12,00,000, the Income in 2015 is also Rs. 12,00,000.

Final Answer

The income of company ABC in 2015 was Rs. 12,00,000.

Revision Table: Key Data and Calculation Steps

Additional Information: Understanding Data Interpretation Questions

Data interpretation questions often require extracting specific information from tables, charts, or graphs and using mathematical formulas or logical reasoning to arrive at an answer. In this case, understanding the formula for percentage profit and carefully reading the conditions given in the question (equal income in 2013 and 2015) were crucial.

Key points to remember when solving data interpretation problems:

• Carefully read the question and identify exactly what is being asked.
• Locate the relevant data in the provided table or chart.
• Understand the definitions of terms used (like profit percentage, investment, income).
• Apply the correct formulas or logic.
• Perform calculations accurately.
• Pay attention to units and any specific conditions mentioned in the question.

This problem involved a straightforward application of the profit percentage formula and a simple equality condition, making the calculation quite direct once the income for 2013 was determined.