This problem involves calculating the amount spent on 'Food' for a college cultural event, given the percentage distribution of expenses and the specific amount spent on 'Tent Items'. We need to use the provided percentage data to find the total cost and then calculate the cost for food.

Expense Percentages Breakdown

The table shows how the total expenses for the cultural event were distributed across different categories:

We are given that the expenses for 'Tent Items' amounted to ₹ 41200.

From the table, we know that 'Tent Items' accounted for 20% of the total expenses.

Total Event Cost Calculation

Let the total expense of organizing the event be $ T $. We can set up the equation based on the information given:

20% of Total Expense = Amount paid for Tent Items

In mathematical terms:

$ 0.20 \times T = ₹ 41200 $

To find the total expense $ T $, we rearrange the equation:

$ T = \frac{₹ 41200}{0.20} $

Calculating the total expense:

$ T = ₹ 41200 \times \frac{1}{0.20} = ₹ 41200 \times 5 = ₹ 206000 $

So, the total amount spent on the cultural event was ₹ 206000.

Food Expense Calculation

Now, we need to find the amount paid for 'Food'. The table indicates that 'Food' expenses were 25% of the total expenses.

Amount paid for Food = 25% of Total Expense

Using the total expense we calculated:

Amount paid for Food = $ 0.25 \times T $

Amount paid for Food = $ 0.25 \times ₹ 206000 $

Calculating the amount:

Amount paid for Food = $ \frac{1}{4} \times ₹ 206000 $

Amount paid for Food = ₹ 51500

Alternatively, we can use the ratio method:

The ratio of the percentage for Food to the percentage for Tent Items is:

$ \frac{\text{Percentage for Food}}{\text{Percentage for Tent Items}} = \frac{25\%}{20\%} = \frac{25}{20} = \frac{5}{4} $

This ratio is equal to the ratio of the amounts spent:

$ \frac{\text{Amount for Food}}{\text{Amount for Tent Items}} = \frac{5}{4} $

Amount for Food = $ \frac{5}{4} \times \text{Amount for Tent Items} $

Amount for Food = $ \frac{5}{4} \times ₹ 41200 $

Amount for Food = $ 5 \times \frac{₹ 41200}{4} $

Amount for Food = $ 5 \times ₹ 10300 $

Amount for Food = ₹ 51500

Therefore, the amount paid for Food was ₹ 51500.