A man earns ₹ 20 on the first day and spends ₹ 15 on the next day. He again earns ₹ 20 on the third day and spends ₹ 15 on the fourth day. If he continues to save like this, how soon will he have ₹ 60 in hand?

### Concept & Logic This is a variation of the classic "monkey climbing a pole" problem. Calculate the net savings over a complete cycle (2 days), but isolate the final step where the target is reached without a subsequent deduction. $$Net\ Cycle\ Savings = Earnings - Spendings$$ ### Step-by-Step Solution * **Given:** * Day 1 Earnings = ₹ 20 * Day 2 Spendings = ₹ 15 * Target Amount = ₹ 60 * **Calculation:** 1. Find the net savings for one complete 2-day cycle: $Net\ Savings = 20 - 15 = 5$ So, in 2 days, the man saves ₹ 5. 2. Identify the target amount needed *before* the final earning day. On the final day, he will earn ₹ 20 and not spend it yet. $Target\ before\ final\ jump = 60 - 20 = 40$ 3. Calculate the time required to accumulate ₹ 40 using the 2-day cycles: Since ₹ 5 is saved every 2 days, the time to save ₹ 40 is $(40 / 5) \times 2 = 16\ days$. 4. By the end of the 16th day, he has exactly ₹ 40 in hand. 5. On the 17th day, he earns ₹ 20. $Total = 40 + 20 = 60$. ### Exam Strategy & Shortcut Always subtract the final positive jump from the total goal first. $60 - 20 = 40$. Determine the rate of progress: ₹ 5 per 2 days. $40 / 5 = 8$ cycles. $8 \times 2 = 16$ days. Add 1 day for the final jump. $16 + 1 = 17$th day. ### Common Pitfall The most common trap is simply dividing the total goal (60) by the net daily savings (5 per 2 days = 2.5/day). Doing $60 / 2.5$ gives 24 days. This fails to account for the fact that on a specific earning day, he hits the goal before the next spending cycle begins. ### Final Answer **Therefore, the correct answer is On 17th day.**