A woman works continuously for 7 days in the kitchen and refuses to work on the 8th day when her husband takes over. If she starts her work on a Sunday, then the 10th time she rests will be on which day of the week?

### Concept & Logic\n\nThe schedule follows a strict recurring cycle. The woman works for 7 days and rests on the 8th day. Thus, each cycle consists of exactly 8 days, and the rest day always occurs on the last day of that cycle.\n\n### Step-by-Step Solution\n\n* **Identify the cycle:**\n * 1 cycle = 7 working days + 1 rest day = 8 days.\n * The rest day of any cycle $n$ occurs at the end of $n$ complete cycles.\n\n* **Find total days elapsed for 10 rest periods:**\n To reach her 10th rest day, she needs to complete exactly 10 full cycles.\n $$\\text{Total days} = 10 \\times 8 = 80 \\text{ days}$$\n\n* **Determine the day of the week:**\n * She starts her first cycle on a **Sunday** (Day 1).\n * The 80th day from the start of the sequence can be found using modular arithmetic (odd days).\n $$\\text{Number of weeks} = \\frac{80}{7} = 11 \\text{ weeks with a remainder of } 3 \\text{ days}$$\n \n Since Day 1 is Sunday, we count forward:\n * Remainder 1 = Sunday\n * Remainder 2 = Monday\n * Remainder 3 = Tuesday\n\n### Exam Strategy & Shortcut\n\nEach cycle is 8 days long. Since $8 \\equiv 1 \\pmod 7$, each cycle shifts the rest day by exactly 1 day of the week forward relative to the cycle's start day cycle positioning.\n* Cycle 1 starts on Sunday $\\rightarrow$ Rest day is Day 8 ($8 \\equiv 1 \\rightarrow$ Sunday).\n* Since each 8-day cycle advances the week day calendar position by 1 day ($8 - 7 = 1$):\n* 10 cycles will advance the rest day by $10 \\times 1 = 10$ days from the base pattern baseline.\n* 10 days $\\equiv 3$ days forward from Sunday $\\rightarrow$ Monday, Tuesday.\n\n### Common Pitfall\n\nStudents often mistakenly calculate the total days as $10 \\times 7 + 10 = 80$, but then add 80 days *to* Sunday (making Sunday = 0), which results in a off-by-one calendar day error. Remember that Day 1 itself is Sunday.\n\n### Final Answer\n\n**Therefore, the correct answer is Tuesday.**