Mohan's Earnings Calculation

This problem involves calculating the day Mohan achieves a specific savings target based on a daily earning and spending pattern. We need to find the day he reaches ₹200 just after earning, but before spending.

Understanding the Daily Cycle

• Mohan earns ₹60 on Day 1, Day 3, Day 5, and so on (odd-numbered days).
• Mohan spends ₹50 on Day 2, Day 4, Day 6, and so on (even-numbered days).

Calculating Net Gain Per Cycle

Consider a 2-day cycle (one earning day + one spending day):

• Total Earned in 2 days = ₹60
• Total Spent in 2 days = ₹50
• Net Gain per 2-day cycle = $60 - 50 = 10$ rupees.

Mohan's savings increase by ₹10 every 2 days.

Determining the Amount Before Final Earning

The target is to have ₹200 *before spending*. This means the amount should reach ₹200 after Mohan earns on an odd-numbered day.

Let the day be 'D'. On day 'D', he earns ₹60. The amount he had at the end of the previous day (Day D-1) plus ₹60 must equal ₹200.

Amount at end of Day (D-1) + $60 = 200$

Amount at end of Day (D-1) = $200 - 60 = 140$ rupees.

So, Mohan needs to accumulate ₹140 by the end of an even-numbered day (the day before he hits the target).

Calculating Cycles to Reach ₹140

Since the net gain is ₹10 per 2-day cycle, the number of cycles needed to reach ₹140 is:

Number of Cycles = $\frac{\text{Target amount before earning}}{\text{Net gain per cycle}} = \frac{140}{10} = 14$ cycles.

Calculating the Number of Days

Each cycle consists of 2 days. Therefore, 14 cycles will take:

Total Days = $14 \text{ cycles} \times 2 \text{ days/cycle} = 28$ days.

At the end of the 28th day (after spending ₹50), Mohan will have ₹140.

Final Step: Reaching ₹200

The day after the 28th day is the 29th day. Day 29 is an earning day.

On the 29th day, Mohan earns ₹60.

His total money becomes: ₹140 (from end of Day 28) + ₹60 (earned on Day 29) = ₹200.

This amount is achieved *before* he spends on Day 29, fulfilling the condition.

Conclusion

Mohan will have ₹200 with him on the $29^{\text{th}}$ day before spending.