Question:
A child was born on 13th January 1976 which was a Tuesday. What day of the week will be the childs birth day in the year 1986?
A child was born on 13th January 1976 which was a Tuesday. What day of the week will be the childs birth day in the year 1986?
Updated On: Jul 15, 2026
- Sunday
- Friday
- Saturday
- Monday
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The Correct Option is D
Approach Solution - 1
The correct option is (D): Monday.
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Approach Solution -2
The question asks what day of the week falls on 13th January 1986, given that 13th January 1976 was a Tuesday. We can work this out by tracking how the day of the week shifts across each of the ten years between the two dates, one year at a time.
- Sunday: To land on Sunday, the total shift across ten years would have to be exactly 5 days forward from Tuesday. Counting the leap years between 1977 and 1986 gives only 3 extra shifts on top of the 10 standard yearly shifts, so this total does not appear.
- Friday: A shift to Friday would need 3 days forward from Tuesday, but the actual count of shifts across this ten year span, worked out below, is larger than 3.
- Saturday: A shift to Saturday would need 4 days forward, again short of the true count for this span.
- Monday: Each ordinary year moves the same date forward by 1 day of the week, and each leap year whose 29th February falls inside the span adds one extra day of shift. Between 13th January 1976 and 13th January 1986, the leap years 1976, 1980, and 1984 each contribute their 29th February within that window, giving 10 ordinary shifts plus 3 extra leap shifts, a total shift of 13 days. Since \( 13 \mod 7 = 6 \), the date moves 6 days forward from Tuesday, landing on Monday.
Working through the year-by-year shift shows a total move of 6 days from Tuesday, which lands exactly on Monday and not on any of the other options.
Therefore, the correct answer is Monday.
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Approach Solution -3
The question gives 13th January 1976 as a Tuesday and asks what day 13th January 1986 falls on. Rather than counting the shift year by year, we can find the exact number of days between the two dates and reduce it modulo 7 to get the day shift directly.
- Sunday: The span from 13th January 1976 to 13th January 1986 covers exactly 10 years, of which 1976, 1980, and 1984 are leap years falling inside the span, giving \( 7 \times 365 + 3 \times 366 = 2555 + 1098 = 3653 \) total days. Dividing, \( 3653 = 7 \times 521 + 6 \), so the remainder is 6, not the 5 that would be needed to land on Sunday.
- Friday: Landing on Friday would require a remainder of 3 days past Tuesday, but the actual remainder calculated from the total day count is 6, so this does not match.
- Saturday: Landing on Saturday would require a remainder of 4, again short of the calculated remainder of 6.
- Monday: With a remainder of 6 days past Tuesday, counting forward Wednesday, Thursday, Friday, Saturday, Sunday, Monday lands exactly on Monday, matching this option.
Dividing the total 3653-day span by 7 leaves a remainder of exactly 6, which shifts Tuesday forward to Monday and rules out every other option.
Therefore, the correct answer is Monday.
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