Cultural Event Expenses: Difference Calculation

This question requires us to calculate the difference between the expenses incurred on 'Food' and 'Poster Making' for a college cultural event. We are given the percentage distribution of expenses across various heads and the total expense amount for the event.

Understanding the Problem

The core task is to find the monetary value difference between two expense categories (Food and Poster Making) based on their respective percentages of the total event expenses.

• Total Expenses: ₹ 67880
• Expense Percentage on Food: 25%
• Expense Percentage on Poster Making: 10%

Step 1: Calculate Food Expenses

First, let's determine the amount spent on Food. We multiply the total expenses by the percentage allocated to Food.

The formula used is:

$$ \text{Expense on Food} = \text{Total Expenses} \times \frac{\text{Percentage of Food Expenses}}{100} $$

Substituting the values:

$$ \text{Expense on Food} = ₹ 67880 \times \frac{25}{100} $$

$$ \text{Expense on Food} = ₹ 67880 \times 0.25 $$

$$ \text{Expense on Food} = ₹ 16970 $$

Step 2: Calculate Poster Making Expenses

Next, we calculate the amount spent on Poster Making using its percentage of the total expenses.

The formula is:

$$ \text{Expense on Poster Making} = \text{Total Expenses} \times \frac{\text{Percentage of Poster Making Expenses}}{100} $$

Substituting the values:

$$ \text{Expense on Poster Making} = ₹ 67880 \times \frac{10}{100} $$

$$ \text{Expense on Poster Making} = ₹ 67880 \times 0.10 $$

$$ \text{Expense on Poster Making} = ₹ 6788 $$

Step 3: Determine the Expense Difference

Now, we find the difference between the expenses calculated for Food and Poster Making.

$$ \text{Difference} = \text{Expense on Food} - \text{Expense on Poster Making} $$

$$ \text{Difference} = ₹ 16970 - ₹ 6788 $$

$$ \text{Difference} = ₹ 10182 $$

Alternative Method (Using Percentage Difference):

We can also find the difference by first calculating the difference in percentages and then applying it to the total expenses.

$$ \text{Difference in Percentage} = \text{Percentage on Food} - \text{Percentage on Poster Making} $$

$$ \text{Difference in Percentage} = 25\% - 10\% = 15\% $$

Now, calculate the amount corresponding to this 15% difference:

$$ \text{Difference} = \text{Total Expenses} \times \frac{\text{Difference in Percentage}}{100} $$

$$ \text{Difference} = ₹ 67880 \times \frac{15}{100} $$

$$ \text{Difference} = ₹ 67880 \times 0.15 $$

$$ \text{Difference} = ₹ 10182 $$

Final Answer Verification

Both methods yield the same result. The difference between the expenses on Food and Poster Making is ₹ 10182.

This value corresponds to option 4.