Manu earns ₹4000 per month and wants to save an average of ₹550 per month in a year. In the first nine months, his monthly expense was ₹3500, and he foresees that, from the tenth month onward, his monthly expense will increase to ₹3700. In order to meet his yearly savings target, his monthly earnings, in rupees, from the tenth month onward should be:

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To solve this problem:

1. **Savings Target**:  
   Manu aims to save ₹550 per month on average for a year, which totals:  
   $$
   	ext{Total Savings Target} = 550 	imes 12 = ₹6600.
   $$

2. **Savings in First 9 Months**:  
   Manu earns ₹4000 per month and spends ₹3500 per month, saving:  
   $$
   	ext{Monthly Savings} = 4000 - 3500 = ₹450.
   $$  
   Over 9 months:  
   $$
   	ext{Total Savings} = 450 	imes 9 = ₹4050.
   $$

3. **Remaining Savings Needed**:  
   To meet the yearly savings target:  
   $$
   	ext{Remaining Savings} = 6600 - 4050 = ₹2550.
   $$

4. **Expenses in Last 3 Months**:  
   Manu’s monthly expenses increase to ₹3700. To save ₹550 per month in these three months, his income should be:  
   $$
   	ext{Required Income} = 3700 + 550 = ₹4250.
   $$

5. **Compensate for Shortfall**:  
   Manu was short by ₹50 per month in the first nine months (as he saved only ₹450 instead of ₹550), totaling a shortfall of:  
   $$
   	ext{Shortfall} = 50 	imes 9 = ₹450.
   $$  
   To cover this shortfall over the next three months, he needs an additional:  
   $$
   \frac{450}{3} = ₹150 	ext{ extra per month}.
   $$

6. **Final Monthly Earnings**:  
   Adding the extra amount to the required income:  
   $$
   	ext{Final Income} = 4250 + 150 = ₹4400.
   $$

Thus, Manu’s monthly earnings from the tenth month onward should be **₹4400**.

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