Question

How many leap years are there in the set of any consecutive 400 years?

Answer 1

Hint: A leap year is the year occurring once every four years and has 366 days. Also, in 100 years there are 24 leap years. A year in which is divisible by 4 and for century years it should be divisible by 400 not 100 then it is said to be leap year. For example 100 is not leap year even though it is divisible by 4 but as it is century year it should be divisible by 400. Hence 100,200,300 are not leap years. Using these conditions calculate the number of years from the given question.

Complete step-by-step answer:
We have been asked in the question to find the leap year in a set of consecutive 400 years.
Now, we know in 100 years there are 24 leap years.
That means, 76 normal years will be there in 100 years.
So, in 100 years, leap year $ = 24$years.
Therefore, in 400 years, leap years will be $
   = 4 \times 24 \\
   = 96 \\
 $
Now, since leap year occurs once after every four years, which means the 400th year is also a leap year.
So, total number of leap year in a set of any consecutive 400 years will be $
   = 96 + 1 \\
   = 97 \\
$
Hence, the answer is 97 leap years.

Note: Whenever such types of questions appear, always know the basic meaning of a leap year and how many times it occurs. This information will be valuable while finding the answer. As mentioned in the solution, in 100 years there are 24 leap years. Hence, we got the answer as 97 leap years in a set of consecutive 400 years.Leap years are any year that can be exactly divided by 4 such as 2016 ,2020 etc.The years which is exactly divided by 100 then it is not leap year such as 2100,2200 etc except if it can be exactly divided by 400 such as 2000 , 2400.In given question 100, 200 and 300 years are not leap year as they divide exactly by 100 but 400 is leap year from the given condition.So we get 24 leap years from 100 years So,for 400 years we get 4 x 24 +1 =97 leap years.