Calculating Total Income Based on Monthly Expenditure and Savings

Understanding your monthly income is essential for financial planning. In this article, we will explore how to calculate a person's total income based on given percentages of expenditure and savings. This is a common scenario in personal and business finance management.

Problem Statement

A person spends 30% of his income on food, 12% on house rent, and 28% on miscellaneous expenses. By the end of the month, he saves Rs 810. What is the person's total income?

Solutions Methodology

Let's consider the given percentages and savings to calculate the total income algebraically. We will present several methods to solve this problem step-by-step, ensuring a thorough understanding of the concept.

Method 1: Percentage and Savings Direct Calculation

We shall determine the total income by first calculating the total percentage of expenses:

Total percentage of expenses 30% (food) 12% (rent) 28% (miscellaneous) 70%

Since the savings is 30% of the total income (100% - 70%), we can set up the following equation:

Let the total income be ( X )

0.3 810

Solving for X:

X 810 / 0.30 2700

Therefore, the person's total income is Rs 2700.

Method 2: Successive Elimination Method

Let's break down the percentages step-by-step using the successive elimination method:

Initial Breakdown:
30% → 3/10
20% → 1/5
20% → 1/5

Further Breakdown:
10 units (u) → 7 units
5 units → 4 units
5 units → 4 units
250 units → 112 units
112 units → 8960
1 unit → 80
250 units → 20000/-

Thus, the total income is Rs 20000/-

Method 3: Direct Saving Percentage Calculation

We can approach this problem by directly considering the savings as a percentage:

Total percentage of expenses 75%
Savings 100% - 75% 25%

If 25% of the savings is Rs 15000, then the total income can be calculated as:

Total income (100 / 25) x 15000 Rs 60000

Method 4: Simplified Calculation Using Savings

Another method to calculate the total income is by recognizing that the savings is a fraction of the total income:

Total expenditure 25% (food) 30% (rent) 20% (miscellaneous) 75%
Savings 100% - 75% 25%

If the savings are Rs 810, which is 25% of the total income, then the total income can be calculated as:

Total income 810 / (1/30) Rs 24000/-

Conclusion

Depending on the available data and the method of calculation, various approaches can accurately determine a person's total income. Understanding these methods not only helps in solving similar problems but also enhances overall financial literacy. By applying these calculations, one can manage personal finances more effectively.