Question:
A child was born on 13th January 1976 which was a Tuesday. What day of the week will be the child’s birthday in the year 1986?
A child was born on 13th January 1976 which was a Tuesday. What day of the week will be the child’s birthday in the year 1986?
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Same date across years: add $+1$ for each ordinary year and $+2$ for each leap year between them, then reduce modulo $7$.
Updated On: Jul 15, 2026
- Sunday
- Friday
- Saturday
- Monday
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The Correct Option is D
Approach Solution - 1
We move from 13 Jan 1976 to 13 Jan 1986 — a span of 10 years. Each ordinary (non-leap) year advances the weekday by $+1$; each leap year adds $+2$ because of the extra day (Feb 29). Since the date is Jan 13, every leap year in between contributes its extra day.
Years crossed and shifts:
\begin{tabular}{l l} 1976 (leap) & $+2$
1977 & $+1$
1978 & $+1$
1979 & $+1$
1980 (leap) & $+2$
1981 & $+1$
1982 & $+1$
1983 & $+1$
1984 (leap) & $+2$
1985 & $+1$
\end{tabular}
[2mm] Total shift $=2+1+1+1+2+1+1+1+2+1=13$ days.
Take $13 \bmod 7 = 6$. Starting from Tuesday, six days ahead is Monday.
Years crossed and shifts:
\begin{tabular}{l l} 1976 (leap) & $+2$
1977 & $+1$
1978 & $+1$
1979 & $+1$
1980 (leap) & $+2$
1981 & $+1$
1982 & $+1$
1983 & $+1$
1984 (leap) & $+2$
1985 & $+1$
\end{tabular}
[2mm] Total shift $=2+1+1+1+2+1+1+1+2+1=13$ days.
Take $13 \bmod 7 = 6$. Starting from Tuesday, six days ahead is Monday.
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Approach Solution -2
The question asks what day of the week 13th January 1986 falls on, given that 13th January 1976 was a Tuesday. Instead of building a year by year table, we can count the total number of days between the two dates and reduce that count modulo 7, then check it against each option.
- Sunday: The span from 13 January 1976 to 13 January 1986 covers 10 full years, made up of 3650 ordinary days plus one extra day for each leap year that falls in between. The leap years 1976, 1980 and 1984 each contribute one extra day, since their 29th of February falls within this ten year window, giving a total of \( 3650 + 3 = 3653 \) days. Dividing \( 3653 \) by 7 leaves a remainder of 6, and moving 6 days forward from Tuesday lands on Monday, not Sunday, so this option does not match.
- Friday: Following the same day count, Friday would need a remainder of 3 days from Tuesday, which does not agree with the calculated remainder of 6, so this is not the answer either.
- Saturday: Saturday would correspond to a remainder of 4 days from Tuesday, again different from the remainder of 6 obtained here, so this can be ruled out.
- Monday: A remainder of 6 days moved forward from Tuesday (Wednesday, Thursday, Friday, Saturday, Sunday, Monday) lands exactly on Monday, matching the day count worked out above.
Counting the total elapsed days and reducing by 7 confirms that only Monday fits the ten year gap between the two dates.
So the correct answer is Monday.
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Approach Solution -3
Instead of tracking every single year from 1976 to 1986, it helps to break the ten-year gap into two five-year chunks, find an intermediate checkpoint date's weekday, and then finish the calculation from there. This also gives a way to double check each of the four given options.
- Sunday: Working from 13 January 1976 (Tuesday) to 13 January 1981 covers the leap years 1976 and 1980, contributing 2 extra days on top of the 5 base years, for a shift of 7, which is a full week and lands back on Tuesday. Continuing another five years to 1986 covers the leap year 1984, giving a further shift of 5 base years plus 1 extra day, that is 6 days, moving from Tuesday to Monday, not Sunday, so this option is ruled out.
- Friday: Following the same two-chunk path, reaching Friday would require a final shift of 3 days from the Tuesday checkpoint in 1981, which does not match the 6-day shift found above.
- Saturday: This would require a shift of 4 days from the 1981 checkpoint, again different from the calculated 6-day shift.
- Monday: The second five-year chunk, 1981 to 1986, produces exactly a 6-day shift from Tuesday, which lands precisely on Monday.
Breaking the period into two five-year blocks and tracking the weekday through an intermediate checkpoint confirms the same result reached directly.
So the correct answer is Monday.
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