Question

Calculate and explain
the number of leap year from 1601 to 1900

Answer 1

To Find :- The number of leap year from 1601 to 1900 ?

Solution :-

Leap year :-

• A leap year is a calendar year that contains an additional day added to keep the calendar year .

How to check a year is a leap year :-

• If last digit of year is divisible by 4 .
• if century year is divisible by 400 .

So,

→ Total leap year in 100 years = (100/4) = 25 years.

• But 100th century is not divisible by 400 .
• Total leap year in 100 years = 25 - 1 = 24 Leap years.

then,

• Total Leap year from 1601 to 1700 = 24
• Total Leap year from 1701 to 1800 = 24
• Total Leap year from 1801 to 1900 = 24

therefore,

• Total Leap year from 1601 to 1900 = 24 + 24 + 24 = 72 Leap years.

Hence, the number of Leap years from 1601 to 1900 are 72 .

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Answer 2

SOLUTION

TO DETERMINE

The number of leap year from 1601 to 1900

EVALUATION

The number of leap years from 1601 to 1900

1604, 1608, 1612, 1616 , ..........,1900

This is an Arithmetic progression with

First term = a = 1604

Common Difference = d = 4

Let there are n numbers of leap year from 1601 to 1900

Then n th term of the AP = 1900

$\implies \sf{a + (n - 1)d = 1900 \: }$

$\implies \sf{1604+ (n - 1)d = 1900 \: }$

$\implies \sf{ 4(n - 1) = 296 \: }$

$\implies \sf{ (n - 1)= 74 \: }$

$\implies \sf{n = 75 \: }$

Hence there are 75 leap years from 1601 to 1900 ( Including 1900 )

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