Question

I bought the January issue of "Vigyan Pragati" in $1986$, which contained the calendar of that year. Which other year can this calendar be used?

• A. $1997$
• B. $2001$
• C. $1995$
• D. $2003$

Answer 1

Answer: (A)

$1997$

In a normal year we have 365 days i.e 52 weeks and one extra day, and in a leap year we have 366 Days i.e 52 weeks and 2 extra days.

So lets assume that we had a Monday on 1st April 1986, so when we will move to 1987 we will get a Tuesday on 1st ( $\because$ one year has 52 weeks and one day which will make 1st as Tuesday), and 1st April 1988 would be a Thursday as it is a leap year so we will get two extra days.
Keep on checking in similar manner, and you will come to a conclusion that the same calender can be used in 1997

Hence, option A.

OR

In a normal year we have 365 days i.e 52 weeks and one extra day, and in a leap year we have 366 Days i.e 52 weeks and 2 extra days.

difference between odd days between the $1986$ and $1997$ = 3 leap yrs + 8 years

= $3\times 2+8$

=$14$

= which is divisible by 7 .

so calender repeats in 1997.