A workman starts on Monday, works for 8 days, and takes every 9th day as a holiday. On which day of the week does his 12th holiday fall?

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Multiple Choice

A workman starts on Monday, works for 8 days, and takes every 9th day as a holiday. On which day of the week does his 12th holiday fall?

Explanation:
The pattern repeats every 9 days: 8 days of work followed by a holiday on the 9th day. So holidays occur on calendar days 9, 18, 27, and so on. The 12th holiday will be on day 9 × 12 = 108. To find the weekday for day 108, note that day 1 is Monday, so the number of days after Monday is 108 − 1 = 107. Since 107 mod 7 = 2, two days after Monday is Wednesday. Therefore, the 12th holiday falls on Wednesday.

The pattern repeats every 9 days: 8 days of work followed by a holiday on the 9th day. So holidays occur on calendar days 9, 18, 27, and so on. The 12th holiday will be on day 9 × 12 = 108.

To find the weekday for day 108, note that day 1 is Monday, so the number of days after Monday is 108 − 1 = 107. Since 107 mod 7 = 2, two days after Monday is Wednesday.

Therefore, the 12th holiday falls on Wednesday.

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