Question

A man has a job which requires him to work eight straight days and rest on the 9th day. If he started work on a Monday, the 12th time he rests will be on what day of the week?

• A. Sunday
• B. Wednesday
• C. Tuesday
• D. Friday

Hint:

When day 1 is known, the weekday of day $d$ is shifted by $(d-1)\bmod 7$. For repeating schedules, first get the exact day number, then apply the mod-7 rule.

Answer 1

The Correct Option is B

Step 1: Model the schedule.
He works for 8 consecutive days, then rests on the 9th day.
So the rest days are day numbers: 9, 18, 27, … i.e., the n-th rest is on day 9n.

Step 2: Find the day number for the 12th rest.
9 × 12 = 108.
So the 12^th rest is on day 108 after starting.

Step 3: Convert a day number to a weekday.
If day 1 is Monday, then the weekday of day d is:
weekday = Monday + (d − 1) mod 7.
For d = 108: compute (108 − 1) mod 7 = 107 mod 7 = 2.
Hence, day 108 is 2 days after Monday ⇒ Wednesday.

Answer: Wednesday