Question

A man has a job which requires him to work 8 straight days and rest on the ninth 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:

The rest days fall on day numbers 9, 18, 27, and so on. Find day number 108, the 12th rest, and count that many days after the starting Monday, using the fact that the week repeats every 7 days.

Answer 1

The Correct Option is B

Step 1: Set up the work rest cycle.
The man works 8 days in a row and then rests on the 9th day, so the full cycle length is 9 days, and every rest day falls on a day number that is a multiple of 9, that is day 9, day 18, day 27, and so on.
He starts work on day 1, which is a Monday.

Step 2: Find the day number of his 12th rest.
The kth rest happens on day number 9k. For the 12th rest,
\[ 9 \times 12 = 108 \]
So the 12th rest falls on day number 108, counting day 1 as the first Monday.

Step 3: Convert day 108 into a weekday.
Since day 1 is a Monday, day n falls on the same weekday as n minus 1 days after Monday. Because the week repeats every 7 days, only the remainder of n minus 1 divided by 7 matters.
\[ 108 - 1 = 107 \]
\[ 107 = 15 \times 7 + 2 \]
So the remainder is 2, meaning day 108 falls 2 weekdays after Monday.

Step 4: Read off the weekday.
Counting 2 days after Monday: 1 day after Monday is Tuesday, 2 days after Monday is Wednesday.

Final Answer:
The 12th rest day falls on a Wednesday.
\[ \boxed{\text{Wednesday}} \]