Calculating Company Expenditure in 2018

The question asks us to determine the approximate expenditure of the company in the year 2018, based on the provided table showing income and profit percentage for six years.

Here is the data table:

Understanding Income, Expenditure, and Profit

The relationship between Income, Expenditure, and Profit is fundamental in business calculations. Profit is the excess of Income over Expenditure.

• Income: The total revenue earned by the company.
• Expenditure: The total cost incurred by the company.
• Profit: Income minus Expenditure (when Income > Expenditure).

The profit percentage is usually calculated with respect to the Expenditure. The formula is:

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

We also know that:

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

Let's denote Income as \(I\), Expenditure as \(E\), and Profit as \(P\). The profit percentage is given as \(p\%\).

From the profit percentage formula, we have \(P = \frac{p}{100} \times E\).

Substituting this into the Income formula:

\(I = E + \frac{p}{100} \times E\)

\(I = E \times \left( 1 + \frac{p}{100} \right)\)

\(I = E \times \left( \frac{100 + p}{100} \right)\)

To find the Expenditure \(E\), we can rearrange the formula:

\(E = I \times \left( \frac{100}{100 + p} \right)\)

Calculating Expenditure for the Year 2018

From the table, we can find the data for the year 2018:

• Income (\(I\)) in 2018 = Rs. 160 lakh
• Profit percentage (\(p\)) in 2018 = 15%

Now, we use the formula for Expenditure:

\(E_{2018} = I_{2018} \times \left( \frac{100}{100 + p_{2018}} \right)\)

Substitute the values for 2018:

\(E_{2018} = 160 \times \left( \frac{100}{100 + 15} \right)\)

\(E_{2018} = 160 \times \left( \frac{100}{115} \right)\)

Simplify the fraction \(\frac{100}{115}\) by dividing both numerator and denominator by 5:

\(\frac{100}{115} = \frac{100 \div 5}{115 \div 5} = \frac{20}{23}\)

So, the calculation becomes:

\(E_{2018} = 160 \times \frac{20}{23}\)

\(E_{2018} = \frac{160 \times 20}{23}\)

\(E_{2018} = \frac{3200}{23}\)

Now, perform the division:

\(\frac{3200}{23} \approx 139.13\)

The calculated expenditure in 2018 is approximately Rs. 139.13 lakh.

The question asks for the approximate expenditure. Comparing Rs. 139.13 lakh with the given options:

• Rs. 120 lakh
• Rs. 160 lakh
• Rs. 140 lakh
• Rs. 180 lakh

Rs. 139.13 lakh is closest to Rs. 140 lakh.

Therefore, the approximate expenditure in 2018 was Rs. 140 lakh.

Revision Table: Key Concepts

Additional Information: Data Interpretation Tips

When solving data interpretation questions involving tables or charts, consider the following tips:

• Read the question carefully to understand exactly what is being asked (e.g., exact value, approximate value, percentage change, ratio).
• Identify the relevant data points from the table or chart for the specific question.
• Understand the units of measurement (e.g., Rs. lakh, percentage).
• Know the basic formulas for profit, loss, percentage, ratio, average, etc.
• Be careful with calculations, especially with percentages and fractions.
• For approximation questions, calculate the exact value first and then find the closest option.
• Practice solving various types of data interpretation problems to improve speed and accuracy.