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Extracted Problem:

Let's consider one of the problems visible in the image:

• Problem 79: The expenditure of a man for the first 3 months is ₹200 and the expenses increase uniformly by ₹40. His expenditure for the next 3 months will be:

  (A) ₹320 (B) ₹360 (C) ₹400 (D) ₹480

Solution:

The problem states that the man’s expenditure increases uniformly by ₹40 each month after the first 3 months. Let's analyze it step by step:

1. Initial 3-month Expenditure:

   • For the first 3 months, his expenditure is ₹200.

2. Monthly Increase:

   • From the 4th month, his monthly expenditure increases by ₹40.

3. Expenditure for Next 3 Months:

   • 4th month: ₹200 + ₹40 = ₹240
   • 5th month: ₹240 + ₹40 = ₹280
   • 6th month: ₹280 + ₹40 = ₹320

4. Total Expenditure for the Next 3 Months:

   • Sum = ₹240 + ₹280 + ₹320 = ₹840

However, since the problem seems to be asking for the monthly expenditure at the end of the 3rd month, the expenditure on the 6th month would be ₹320.

So, the correct answer for the monthly expenditure at the end of 6 months would be ₹320 (Option A).

Additional Questions:

1. If the expenditure increases by ₹50 each month instead of ₹40, what would be the expenditure for the next 3 months?
2. What would be the total expenditure for the first 6 months?
3. How would the expenditure change if the initial expenditure was ₹300 instead of ₹200?
4. If the expenditure was calculated for 12 months instead of 6, how would you approach the problem?
5. How can the concept of arithmetic progression be applied to solve this problem more generally?

Tip: Always double-check the terms and structure of arithmetic progressions when dealing with uniformly increasing or decreasing sequences.