Understanding the Income and Expenditure Data

The question provides a table showing the monthly income and various expenditures for six friends (A-F). Some values are missing, indicated by a dash (-). We are also given important notes that define the relationship between Salary, Incentive, Monthly Income, Savings, and Expenditures.

The goal is to calculate the difference between the combined expenditure of friend B on Food and Shopping and the expenditure of friend C on Accommodation.

Let's first understand the key relationships provided in the notes:

• Monthly Income = Salary + Incentive
• Incentive = 15% of Salary
• Savings = 40% of Monthly Income
• Total Expenditure = Monthly Income - Savings
• Total Expenditure = Sum of expenditures on Travel, Food, Accommodation, and Shopping.

To solve this problem, we need to calculate the missing values for friends B and C, specifically their Monthly Income and the required expenditure amounts (Shopping for B and Accommodation for C).

Calculating Values for Friend B

From the table, we know the Incentive for B is Rs. 14400. Using note (b):

Incentive = 15% of Salary

\(14400 = 0.15 \times \text{Salary}_B\)

We can calculate Salary for B:

\(\text{Salary}_B = \frac{14400}{0.15}\)

\(\text{Salary}_B = 96000\)

Now, using note (a), we find the Monthly Income for B:

\(\text{Monthly Income}_B = \text{Salary}_B + \text{Incentive}_B\)

\(\text{Monthly Income}_B = 96000 + 14400\)

\(\text{Monthly Income}_B = 110400\)

According to note (c), B saves 40% of their monthly income:

\(\text{Savings}_B = 40\% \times \text{Monthly Income}_B\)

\(\text{Savings}_B = 0.40 \times 110400\)

\(\text{Savings}_B = 44160\)

Using note (d), the Total Expenditure for B is:

\(\text{Total Expenditure}_B = \text{Monthly Income}_B - \text{Savings}_B\)

\(\text{Total Expenditure}_B = 110400 - 44160\)

\(\text{Total Expenditure}_B = 66240\)

The table gives the expenditures for B on Travel (15280), Food (17000), and Accommodation (12400). Shopping is missing. Using the relationship that Total Expenditure is the sum of all expenditures:

\(\text{Total Expenditure}_B = \text{Travel}_B + \text{Food}_B + \text{Accommodation}_B + \text{Shopping}_B\)

\(66240 = 15280 + 17000 + 12400 + \text{Shopping}_B\)

\(66240 = 44680 + \text{Shopping}_B\)

Now, we find the Shopping expenditure for B:

\(\text{Shopping}_B = 66240 - 44680\)

\(\text{Shopping}_B = 21560\)

The amount spent by B on Food and Shopping together is:

\(\text{Food}_B + \text{Shopping}_B = 17000 + 21560\)

\(\text{Food}_B + \text{Shopping}_B = 38560\)

Calculating Values for Friend C

From the table, we know the Incentive for C is Rs. 12600. Using note (b):

Incentive = 15% of Salary

\(12600 = 0.15 \times \text{Salary}_C\)

We can calculate Salary for C:

\(\text{Salary}_C = \frac{12600}{0.15}\)

\(\text{Salary}_C = 84000\)

Now, using note (a), we find the Monthly Income for C:

\(\text{Monthly Income}_C = \text{Salary}_C + \text{Incentive}_C\)

\(\text{Monthly Income}_C = 84000 + 12600\)

\(\text{Monthly Income}_C = 96600\)

According to note (c), C saves 40% of their monthly income. This means C spends 100% - 40% = 60% of their monthly income on total expenditure.

\(\text{Total Expenditure}_C = 60\% \times \text{Monthly Income}_C\)

\(\text{Total Expenditure}_C = 0.60 \times 96600\)

\(\text{Total Expenditure}_C = 57960\)

The table gives the expenditures for C as percentages of monthly income for Travel (12%), Food (8%), and Shopping (12%). Accommodation is missing.

The sum of the given expenditure percentages for C is:

\(\text{Travel Percentage} + \text{Food Percentage} + \text{Shopping Percentage}\)

\(12\% + 8\% + 12\% = 32\%\)

Since the total expenditure is 60% of the monthly income (as calculated from savings), the remaining percentage must be for Accommodation:

\(\text{Accommodation Percentage}_C = \text{Total Expenditure Percentage} - (\text{Travel Percentage} + \text{Food Percentage} + \text{Shopping Percentage})\)

\(\text{Accommodation Percentage}_C = 60\% - 32\%\)

\(\text{Accommodation Percentage}_C = 28\%\)

Now, we calculate the amount spent by C on Accommodation:

\(\text{Accommodation}_C = 28\% \times \text{Monthly Income}_C\)

\(\text{Accommodation}_C = 0.28 \times 96600\)

\(\text{Accommodation}_C = 27048\)

Calculating the Difference

We need to find the difference between the amount spent by B on Food and Shopping together (38560) and the amount spent by C on Accommodation (27048).

\(\text{Difference} = (\text{Food}_B + \text{Shopping}_B) - \text{Accommodation}_C\)

\(\text{Difference} = 38560 - 27048\)

\(\text{Difference} = 11512\)

The difference in the amount spent is Rs. 11,512.

Revision Table - Key Calculations for B and C

Additional Information - Income, Expenditure, and Savings Concepts

This problem involves basic concepts of personal finance often used in data interpretation questions. Understanding these relationships is key to solving such problems.

• Monthly Income: This is the total money earned in a month, which in this case is the sum of salary and any incentives.
• Expenditure: These are the costs incurred on various items like travel, food, accommodation, and shopping. Total expenditure is the sum of all these individual expenditures.
• Savings: This is the portion of the income that is not spent. It is calculated as Monthly Income minus Total Expenditure. The problem states that savings are a fixed percentage of the monthly income for all friends (40%).
• Percentage Calculations: Many values are given as percentages of monthly income. Converting these percentages to absolute values (and vice versa) is a crucial step in solving the problem. For example, 10% of Rs. 92000 is \(0.10 \times 92000 = 9200\).
• Missing Data: The dash (-) indicates missing data points. The problem setup provides enough information through the notes and other data points to calculate these missing values.

By consistently applying the given rules and relationships, we can fill in the missing information and answer specific questions about the data.