Understanding the Data Interpretation Problem

The question provides a table showing the Income and Expenditure for five different companies (A, B, C, D, and E) in the year 2021. It also gives the formula to calculate the profit or loss percentage:
\( \text{(Profit/Loss) \%} = \left[ \frac{\text{Income} - \text{Expenditure}}{\text{Expenditure}} \right] \times 100 \)

We need to focus on Company E and determine its income in the year 2020, given specific information about its expenditure change from 2020 to 2021 and its profit percentage in 2020.

Analyzing Company E's Data from the Table (2021)

Let's extract the relevant data for Company E from the provided table:

So, for Company E in 2021:

• Income (\(I_{2021}\)) = 50 million Rs.
• Expenditure (\(E_{2021}\)) = 45 million Rs.

Calculating Company E's Expenditure in 2020

The question states that Company E's expenditure in 2021 had increased by 20% from the year 2020.

Let \(E_{2020}\) be the expenditure of Company E in 2020.

The expenditure in 2021 is \(E_{2020}\) plus a 20% increase on \(E_{2020}\).

This can be written as:

\( E_{2021} = E_{2020} + 20\% \text{ of } E_{2020} \)

\( E_{2021} = E_{2020} + \frac{20}{100} \times E_{2020} \)

\( E_{2021} = E_{2020} \times \left( 1 + \frac{20}{100} \right) \)

\( E_{2021} = E_{2020} \times (1 + 0.20) \)

\( E_{2021} = 1.20 \times E_{2020} \)

We know \(E_{2021} = 45\) million Rs. Substitute this value into the equation:

\( 45 = 1.20 \times E_{2020} \)

Now, solve for \(E_{2020}\):

\( E_{2020} = \frac{45}{1.20} \)

\( E_{2020} = \frac{45}{\frac{120}{100}} = \frac{45 \times 100}{120} = \frac{4500}{120} \)

\( E_{2020} = \frac{450}{12} = \frac{150}{4} = 37.5 \)

So, Company E's expenditure in 2020 was 37.5 million Rs.

Calculating Company E's Income in 2020

The question states that Company E had a profit of 10% in the year 2020.

Let \(I_{2020}\) be the income of Company E in 2020.

Using the profit percentage formula for 2020:

\( \text{Profit \% in 2020} = \left[ \frac{I_{2020} - E_{2020}}{E_{2020}} \right] \times 100 \)

We are given that Profit % in 2020 is 10%, and we calculated \(E_{2020} = 37.5\).

\( 10 = \left[ \frac{I_{2020} - 37.5}{37.5} \right] \times 100 \)

Divide both sides by 100:

\( \frac{10}{100} = \frac{I_{2020} - 37.5}{37.5} \)

\( 0.10 = \frac{I_{2020} - 37.5}{37.5} \)

Multiply both sides by 37.5:

\( 0.10 \times 37.5 = I_{2020} - 37.5 \)

\( 3.75 = I_{2020} - 37.5 \)

Now, solve for \(I_{2020}\) by adding 37.5 to both sides:

\( I_{2020} = 3.75 + 37.5 \)

\( I_{2020} = 41.25 \)

So, Company E's income in 2020 was 41.25 million Rs.

Summary of Calculation Steps

• Identify Company E's expenditure in 2021 from the table (\(E_{2021} = 45\)).
• Use the percentage increase information to find Company E's expenditure in 2020 (\(E_{2020}\)). \(E_{2020} = E_{2021} / 1.20\).
• Use the profit percentage in 2020 (10%) and the calculated \(E_{2020}\) to find Company E's income in 2020 (\(I_{2020}\)). The profit formula is used: \(I_{2020} = E_{2020} + 10\% \text{ of } E_{2020} = 1.10 \times E_{2020}\).
• Perform the calculations: \(E_{2020} = 45 / 1.20 = 37.5\). \(I_{2020} = 1.10 \times 37.5 = 41.25\).

The company's income in 2020 was 41.25 million Rs.

Revision Table: Key Calculations for Company E

Additional Information: Profit and Loss Concepts

Understanding profit, loss, income, and expenditure is fundamental in business and data analysis. Here's a quick recap:

• Income: The total revenue or money earned by a company from its operations.
• Expenditure: The total costs or money spent by a company during its operations.
• Profit: Occurs when Income is greater than Expenditure (\(\text{Income} > \text{Expenditure}\)). The profit amount is \(\text{Income} - \text{Expenditure}\).
• Loss: Occurs when Expenditure is greater than Income (\(\text{Expenditure} > \text{Income}\)). The loss amount is \(\text{Expenditure} - \text{Income}\).
• Profit Percentage: Calculated as \(\left[ \frac{\text{Profit}}{\text{Expenditure}} \right] \times 100\).
• Loss Percentage: Calculated as \(\left[ \frac{\text{Loss}}{\text{Expenditure}} \right] \times 100\).

The given formula \( \left[ \frac{\text{Income} - \text{Expenditure}}{\text{Expenditure}} \right] \times 100 \) correctly represents both profit and loss percentage. If Income > Expenditure, the numerator is positive (profit). If Income < Expenditure, the numerator is negative (loss).

When dealing with percentage changes year-on-year, remember that the percentage change is usually calculated with respect to the previous year's value. If something increases by X%, the new value is the original value multiplied by \((1 + X/100)\). If it decreases by X%, the new value is the original value multiplied by \((1 - X/100)\).