This problem involves analyzing financial data for companies, specifically income, expenditure, and profit percentages, based on the provided table.

The formula given for calculating the percent profit or loss is:

\(\text{(Profit/Loss) \%} = \left[\frac{\text{Income - Expenditure}}{\text{Expenditure}}\right] \times 100\)

A positive result indicates a profit, while a negative result indicates a loss.

Understanding the Company D Financial Data Question

The question focuses specifically on Company D and asks about its expenditure in the year 2020. We are given two key pieces of information relating 2021 data to 2020 data for Company D:

• The income of Company D in 2021 was 10% more than its income in 2020.
• Company D earned a profit of 20% in 2020.

Calculating Company D's Income in 2020

First, let's find the income of Company D in 2020. From the table, we see that the income of Company D in 2021 is 40 million Rs.

Let \(I_{2021}\) be the income in 2021 and \(I_{2020}\) be the income in 2020.

We are told \(I_{2021}\) was 10% more than \(I_{2020}\). This can be written as:

\(I_{2021} = I_{2020} + 10\%\text{ of } I_{2020}\)

\(I_{2021} = I_{2020} + 0.10 \times I_{2020}\)

\(I_{2021} = (1 + 0.10) \times I_{2020}\)

\(I_{2021} = 1.10 \times I_{2020}\)

We know \(I_{2021} = 40\) million Rs. So, we can solve for \(I_{2020}\):

\(40 = 1.10 \times I_{2020}\)

\(I_{2020} = \frac{40}{1.10} = \frac{400}{11}\) million Rs.

Calculating Company D's Expenditure in 2020

Next, we use the information about the profit in 2020. Company D had a profit of 20% in 2020. We will use the profit percentage formula:

\(\text{Profit \%} = \left[\frac{\text{Income - Expenditure}}{\text{Expenditure}}\right] \times 100\)

Let \(E_{2020}\) be the expenditure in 2020. For the year 2020:

\(20 = \left[\frac{I_{2020} - E_{2020}}{E_{2020}}\right] \times 100\)

Substitute the value of \(I_{2020} = \frac{400}{11}\):

\(20 = \left[\frac{\frac{400}{11} - E_{2020}}{E_{2020}}\right] \times 100\)

Divide both sides by 100:

\(\frac{20}{100} = \frac{\frac{400}{11} - E_{2020}}{E_{2020}}\)

\(0.20 = \frac{\frac{400}{11} - E_{2020}}{E_{2020}}\)

Multiply both sides by \(E_{2020}\):

\(0.20 \times E_{2020} = \frac{400}{11} - E_{2020}\)

Add \(E_{2020}\) to both sides:

\(0.20 \times E_{2020} + E_{2020} = \frac{400}{11}\)

\((0.20 + 1) \times E_{2020} = \frac{400}{11}\)

\(1.20 \times E_{2020} = \frac{400}{11}\)

Solve for \(E_{2020}\):

\(E_{2020} = \frac{\frac{400}{11}}{1.20}\)

\(E_{2020} = \frac{400}{11 \times 1.20}\)

\(E_{2020} = \frac{400}{13.2}\)

To make the calculation easier, multiply the numerator and denominator by 10:

\(E_{2020} = \frac{4000}{132}\)

This fraction can be simplified by dividing both by 4:

\(E_{2020} = \frac{1000}{33}\)

Now, let's calculate the approximate value:

\(E_{2020} \approx 30.3030...\)

The expenditure of Company D in 2020 was approximately 30.30 million Rs.

Comparing with Options

Let's compare our calculated approximate expenditure with the given options:

• 28.28
• 30.30
• 32.32
• 34.34

Our calculated value of approximately 30.30 million Rs. matches the second option exactly.

Revision Table: Company D Financials

Additional Information on Profit and Loss Calculations

The formula for profit or loss percentage is a fundamental concept in business and financial analysis. It helps in understanding the profitability or efficiency of a company's operations relative to its expenses.

• Profit: Occurs when Income > Expenditure. The profit amount is (Income - Expenditure).
• Loss: Occurs when Income < Expenditure. The loss amount is (Expenditure - Income). The loss percentage is calculated using the same formula, but the result will be negative, or sometimes the formula is modified to show a positive percentage loss: \(\text{Loss \%} = \left[\frac{\text{Expenditure - Income}}{\text{Expenditure}}\right] \times 100\). However, the question's formula handles both with a sign difference.
• Break-even: Occurs when Income = Expenditure. Profit/Loss % = 0%.

When working with percentage increases or decreases in values over time:

• If a value increases by X%, the new value is Original Value \(\times (1 + \frac{X}{100})\).
• If a value decreases by X%, the new value is Original Value \(\times (1 - \frac{X}{100})\).

In this problem, the 2021 income was 10% more than the 2020 income, so \(I_{2021} = I_{2020} \times (1 + \frac{10}{100}) = I_{2020} \times 1.10\), which is what we used.

Also, from the profit formula, \(20 = \left[\frac{I_{2020} - E_{2020}}{E_{2020}}\right] \times 100\). This can be rewritten as \(0.20 = \frac{I_{2020}}{E_{2020}} - 1\). Adding 1 to both sides gives \(1.20 = \frac{I_{2020}}{E_{2020}}\). This means \(I_{2020} = 1.20 \times E_{2020}\). In other words, the income was 120% of the expenditure, or the income was the expenditure plus a 20% profit on the expenditure.

This confirms our equation \(1.20 \times E_{2020} = I_{2020}\) used in the calculation.