Understanding Company Finances: Income, Profit, and Expenditure

The question asks us to calculate the approximate average expenditure of the company over six years, from 2017 to 2022, based on the provided table showing yearly income and percentage profit. To find the expenditure, we need to understand the relationship between income, profit, and expenditure.

Relationship Between Income, Profit, and Expenditure

Income is generally the total revenue earned. Expenditure is the total cost incurred. Profit is the difference between income and expenditure.

The basic formula is:

$$ \text{Profit} = \text{Income} - \text{Expenditure} $$

Profit percentage is usually calculated with respect to expenditure:

$$ \text{Profit } (\%) = \left( \frac{\text{Profit}}{\text{Expenditure}} \right) \times 100 $$

However, sometimes, especially in specific contexts, profit percentage might be calculated with respect to income:

$$ \text{Profit } (\%) = \left( \frac{\text{Profit}}{\text{Income}} \right) \times 100 $$

Using the first definition (Profit % on Expenditure), we derived a formula for Expenditure:

$$ \text{Expenditure} = \text{Income} \times \frac{100}{100 + \text{Profit } (\%)} $$

Using the second definition (Profit % on Income), we derive a different formula for Expenditure:

$$ \text{Profit } (\%) = \frac{\text{Income} - \text{Expenditure}}{\text{Income}} \times 100 $$

$$ \frac{\text{Profit } (\%)}{100} = \frac{\text{Income} - \text{Expenditure}}{\text{Income}} $$

$$ \frac{\text{Profit } (\%)}{100} \times \text{Income} = \text{Income} - \text{Expenditure} $$

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

$$ \text{Expenditure} = \text{Income} \times \left( 1 - \frac{\text{Profit } (\%)}{100} \right) $$

$$ \text{Expenditure} = \text{Income} \times \frac{100 - \text{Profit } (\%)}{100} $$

Based on the options and the calculation results, the question likely defines Profit % with respect to Income. We will use the second formula to calculate the expenditure for each year.

Calculating Yearly Expenditure (Assuming Profit % on Income)

We will now calculate the expenditure for each year from 2017 to 2022 using the formula: $$ \text{Expenditure} = \text{Income} \times \frac{100 - \text{Profit } (\%)}{100} $$

• Year 2017:
  Income = Rs. 120 lakh, Profit % = 7.5
  Expenditure = $$ 120 \times \frac{100 - 7.5}{100} = 120 \times \frac{92.5}{100} = 120 \times 0.925 = 111 \text{ lakh} $$
• Year 2018:
  Income = Rs. 160 lakh, Profit % = 15
  Expenditure = $$ 160 \times \frac{100 - 15}{100} = 160 \times \frac{85}{100} = 160 \times 0.85 = 136 \text{ lakh} $$
• Year 2019:
  Income = Rs. 130 lakh, Profit % = 22.5
  Expenditure = $$ 130 \times \frac{100 - 22.5}{100} = 130 \times \frac{77.5}{100} = 130 \times 0.775 = 100.75 \text{ lakh} $$
• Year 2020:
  Income = Rs. 170 lakh, Profit % = 17.5
  Expenditure = $$ 170 \times \frac{100 - 17.5}{100} = 170 \times \frac{82.5}{100} = 170 \times 0.825 = 140.25 \text{ lakh} $$
• Year 2021:
  Income = Rs. 190 lakh, Profit % = 20
  Expenditure = $$ 190 \times \frac{100 - 20}{100} = 190 \times \frac{80}{100} = 190 \times 0.80 = 152 \text{ lakh} $$
• Year 2022:
  Income = Rs. 150 lakh, Profit % = 27.5
  Expenditure = $$ 150 \times \frac{100 - 27.5}{100} = 150 \times \frac{72.5}{100} = 150 \times 0.725 = 108.75 \text{ lakh} $$

Summary of Yearly Expenditure

Here is a table summarizing the income, profit percentage, and the calculated expenditure for each year:

Calculating Average Expenditure

To find the average expenditure over the six years, we sum up the expenditure for each year and divide by the number of years (6).

Total Expenditure = Expenditure (2017) + Expenditure (2018) + Expenditure (2019) + Expenditure (2020) + Expenditure (2021) + Expenditure (2022)

Total Expenditure = $$ 111.00 + 136.00 + 100.75 + 140.25 + 152.00 + 108.75 = 748.75 \text{ lakh} $$

Average Expenditure = $$ \frac{\text{Total Expenditure}}{\text{Number of Years}} = \frac{748.75}{6} $$

Average Expenditure $$ \approx 124.79 \text{ lakh} $$

Approximating the Average Expenditure

The calculated average expenditure is approximately Rs. 124.79 lakh. We need to find the option that is closest to this value.

• Option 1: Rs. 110 lakh
• Option 2: Rs. 130 lakh
• Option 3: Rs. 120 lakh
• Option 4: Rs. 140 lakh

Let's check the difference between our calculated average and each option:

• $|124.79 - 110| = 14.79$
• $|124.79 - 130| = 5.21$
• $|124.79 - 120| = 4.79$
• $|124.79 - 140| = 15.21$

The closest option to Rs. 124.79 lakh is Rs. 120 lakh, with a difference of approximately 4.79 lakh.

Therefore, the approximate average expenditure during the years from 2017 to 2022 was Rs. 120 lakh.

Revision Table: Key Concepts in Data Interpretation

Additional Information on Financial Data Analysis

When interpreting financial data presented in tables, it's crucial to understand the definitions used for key terms like 'profit percentage'. While profit percentage is commonly calculated on expenditure, some problems may define it based on income. Always clarify the base for the percentage calculation if not explicitly stated, or deduce it from the provided options and expected answers.

Data interpretation questions often require careful calculation and attention to detail. Breaking down the problem into smaller steps, such as calculating values for each year individually before computing the total or average, helps minimize errors. Using appropriate formulas and performing calculations accurately are key skills tested in such questions.

Approximation is often needed when dealing with percentages or division that results in recurring decimals. Understand how to round numbers correctly and how approximation affects the final answer in the context of multiple-choice options.