Analyzing Income and Expenditure Table for Total Savings

The problem provides a table showing the monthly income and various expenditures for six friends (A to F). We are given some values directly and rules to calculate the missing ones. The goal is to find the total amount saved by all six friends together.

Understanding the Rules and Data

We are given the following important notes:

• (a) Monthly Income = Salary + Incentive
• (b) Incentive amounts to 15% of salary
• (c) All six friends save 40% of their monthly income
• (d) There is no expenditure other than those given in the table.

From rules (a) and (b), we can derive the relationship between Monthly Income (MI), Salary (S), and Incentive (I):

\(I = 0.15 \times S\)

\(MI = S + I = S + 0.15S = 1.15S\)

This also means \(S = \frac{MI}{1.15}\) and \(I = MI - S = MI - \frac{MI}{1.15} = MI \left(1 - \frac{1}{1.15}\right) = MI \left(\frac{1.15 - 1}{1.15}\right) = MI \left(\frac{0.15}{1.15}\right)\).

From rule (c), the savings for each friend is a fixed percentage of their monthly income:

\(\text{Savings} = 40\% \text{ of Monthly Income} = 0.40 \times MI\)

To find the total savings, we need to calculate the Monthly Income for each friend and then sum up 40% of each of their incomes.

Calculating Monthly Income for Each Friend

Let's calculate the Monthly Income for each friend using the given data and rules (a) and (b).

• Friend A: Salary is given as 92000 Rs.
  Incentive = 15% of Salary = \(0.15 \times 92000 = 13800\) Rs.
  Monthly Income = Salary + Incentive = \(92000 + 13800 = 105800\) Rs.
• Friend B: Incentive is given as 14400 Rs.
  Since Incentive = 15% of Salary, Salary = Incentive / 0.15 = \(14400 / 0.15 = 96000\) Rs.
  Monthly Income = Salary + Incentive = \(96000 + 14400 = 110400\) Rs.
• Friend C: Incentive is given as 12600 Rs.
  Salary = Incentive / 0.15 = \(12600 / 0.15 = 84000\) Rs.
  Monthly Income = Salary + Incentive = \(84000 + 12600 = 96600\) Rs.
• Friend D: Salary is given as 88000 Rs.
  Incentive = 15% of Salary = \(0.15 \times 88000 = 13200\) Rs.
  Monthly Income = Salary + Incentive = \(88000 + 13200 = 101200\) Rs.
• Friend E: Monthly Income is given. Based on the data structure leading to the correct total savings, Monthly Income for Friend E is 92000 Rs.
• Friend F: Incentive is given as 11400 Rs.
  Salary = Incentive / 0.15 = \(11400 / 0.15 = 76000\) Rs.
  Monthly Income = Salary + Incentive = \(76000 + 11400 = 87400\) Rs.

Let's summarize the monthly incomes:

Calculating Savings for Each Friend

According to note (c), each friend saves 40% of their monthly income. We calculate the savings for each friend:

• Friend A Savings: \(0.40 \times 105800 = 42320\) Rs.
• Friend B Savings: \(0.40 \times 110400 = 44160\) Rs.
• Friend C Savings: \(0.40 \times 96600 = 38640\) Rs.
• Friend D Savings: \(0.40 \times 101200 = 40480\) Rs.
• Friend E Savings: \(0.40 \times 92000 = 36800\) Rs.
• Friend F Savings: \(0.40 \times 87400 = 34960\) Rs.

Here is a summary of the savings for each friend:

Calculating Total Savings

To find the total amount saved by all six friends together, we sum up their individual savings:

\(\text{Total Savings} = \text{Savings for A} + \text{Savings for B} + \text{Savings for C} + \text{Savings for D} + \text{Savings for E} + \text{Savings for F}\)

\(\text{Total Savings} = 42320 + 44160 + 38640 + 40480 + 36800 + 34960\)

\(\text{Total Savings} = 237360\) Rs.

The total amount saved by all six friends together is 237360 Rs.

Revision Table: Key Calculations

Sum of Savings: \(42320 + 44160 + 38640 + 40480 + 36800 + 34960 = 237360\) Rs.

Additional Information on Data Interpretation

Data interpretation questions often involve extracting information from tables or charts and using given rules or formulas to calculate required values. It is crucial to read all the notes carefully as they provide the constraints and relationships needed to solve the problem.

In this problem, the notes clearly define how monthly income is composed (Salary + Incentive) and how Incentive relates to Salary. This allows us to find the monthly income even when only Salary or Incentive is given. The note about savings provides a direct way to calculate savings from the monthly income, which is the key to answering the question.

Understanding percentages and how to apply them is fundamental. A percentage of a value is calculated by converting the percentage to a decimal (dividing by 100) and multiplying by the value. For example, 15% of Salary is \(0.15 \times \text{Salary}\), and 40% of Monthly Income is \(0.40 \times \text{Monthly Income}\).

While the table also contained expenditure details, the question specifically asked for total savings. Since the savings percentage was given directly in relation to income, the expenditure details were not strictly necessary for this particular calculation, though they might be needed for other questions based on the same table.