Ram spent 4500 per month for 7 months and made some savings. Thereafter he began to spend 5700 per month. At the end of the year he had no savings. Find Ram's monthly income.

Let's solve this step by step.

### Step 1: Total period of time
- Ram spends for a total of 12 months (1 year).

### Step 2: Expenses during the first 7 months
- For the first 7 months, Ram spends 4500 per month.
- Total expenditure for the first 7 months:
  \[
  4500 \times 7 = 31,500
  \]

### Step 3: Expenses during the remaining 5 months
- For the next 5 months, Ram spends 5700 per month.
- Total expenditure for the last 5 months:
  \[
  5700 \times 5 = 28,500
  \]

### Step 4: Total expenses for the entire year
- Adding both expenses together gives the total expenditure for the entire year:
  \[
  31,500 + 28,500 = 60,000
  \]

### Step 5: Income calculation
- Let Ram's monthly income be \( x \).
- His income for the entire year is \( 12 \times x = 12x \).
- According to the problem, at the end of the year he had no savings, meaning his total income equals his total expenses.
  
So we can write the equation:
\[
12x = 60,000
\]

### Step 6: Solve for \( x \)
\[
x = \frac{60,000}{12} = 5,000
\]

### Final Answer:
Ram's monthly income is ₹5,000.

Would you like further details or have any questions?

Here are some related questions for practice:
1. If Ram had saved ₹1000 by the end of the year, what would his monthly income be?
2. What would Ram's total expenditure be if he spent ₹6000 per month for the whole year?
3. If Ram received a bonus of ₹12,000 after 12 months, how would this affect his income?
4. How much would Ram save if his income was ₹5500 per month and his expenditure remained the same?
5. If Ram's expenses increased to ₹6000 per month for the last 5 months, how would this impact his total expenses?

**Tip**: Break down time periods and expenses step-by-step to avoid confusion in budget-related problems.

Find Ram's monthly income using linear equations and basic arithmetic. Ram spent ₹4500 for 7 months and ₹5700 for the remaining 5 months, leaving him with no savings at the end of the year. Suitable for students in Grades 6-8.

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