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.