Math Problem Statement

A person spends 97% of their income, saving 3%. If their savings are Rs. 600, find their income. Another person saves 10% of their income and spends Rs. 15,000. Calculate their income.

Solution

The text from the image describes two scenarios regarding a person's income and savings:

  1. A person spends 97% of their income, leaving a saving of 3%. If their monthly savings are Rs. 600, the task is to find their total monthly income.
  2. A person saves 10% of their income, meaning they spend 90%. If their monthly expenditure is Rs. 15,000, the task is to determine their total monthly income.

Let me calculate both:


Case 1: Savings of Rs. 600 with 3% savings

Let the monthly income be xx. Savings are 3%3\% of income: 0.03x=6000.03x = 600 Solve for xx: x=6000.03=20,000x = \frac{600}{0.03} = 20,000 The total monthly income is Rs. 20,000.


Case 2: Expenditure of Rs. 15,000 with 90% spending

Let the monthly income be yy. Expenditure is 90%90\% of income: 0.9y=15,0000.9y = 15,000 Solve for yy: y=15,0000.9=16,667y = \frac{15,000}{0.9} = 16,667 The total monthly income is Rs. 16,667.


Summary:

  1. In the first case, the income is Rs. 20,000.
  2. In the second case, the income is Rs. 16,667.

Do you need further clarification or detailed steps?

Follow-up questions:

  1. What other percentages of savings or expenditures should be calculated?
  2. How would the results change if savings percentages varied?
  3. What is the difference in income between these two cases?
  4. Can you derive a general formula for income based on savings or expenditures?
  5. Would you like a visual representation of these calculations?

Tip:

Always express savings or expenditures as a fraction or percentage of total income to simplify such problems!

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Math Problem Analysis

Mathematical Concepts

Percentage calculations
Algebraic equations

Formulas

Savings = (Savings Percentage / 100) × Income
Expenditure = (Expenditure Percentage / 100) × Income

Theorems

Basic percentage theorem

Suitable Grade Level

Grades 6-8