How many leap years are there in 100 - 200 - 300 - 400 years?
Q1. How many leap years are there in 100 years ? ā§§ā§Ļā§Ļ āĻŦāĻā§°āĻ¤ āĻāĻŋāĻŽāĻžāĻ¨āĻāĻž Leap Year āĻĨāĻžāĻā§ ?
Soln
- Normally, 1 leap year in every 4 years
- So, 100 ÷ 4 = 25
- 100 is a century year
- A century year is a leap year only if divisible by 400
- 100 is NOT divisible by 400
- Therefore, 1 leap year is reduced
Ans: 25 − 1 = 24 leap years
āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨ :
- āĻ¸āĻžāĻ§āĻžā§°āĻŖāĻ¤ā§ āĻĒā§ā§°āĻ¤ā§āĻ¯ā§āĻ ā§Ē āĻŦāĻā§°āĻ¤ ā§§āĻāĻž Leap Year
- āĻ¸ā§āĻ¯āĻŧā§, 100 ÷ 4 = 25
- 100 āĻāĻāĻž āĻļāĻ¤āĻŋāĻāĻž āĻŦāĻā§°
- āĻļāĻ¤āĻŋāĻāĻž āĻŦāĻā§° āĻā§ā§ąāĻ˛ ā§Ēā§Ļā§Ļā§°ā§ āĻŦāĻŋāĻāĻžāĻā§āĻ¯ āĻš’āĻ˛ā§ Leap Year āĻšāĻ¯āĻŧ
- 100, 400ā§°ā§ āĻŦāĻŋāĻāĻžāĻā§āĻ¯ āĻ¨āĻšāĻ¯āĻŧ
- āĻ¸ā§āĻ¯āĻŧā§ ā§§āĻāĻž Leap Year āĻŦāĻžāĻĻ
āĻāĻ¤ā§āĻ¤ā§°: 24āĻāĻž Leap Year
Q2. How many leap years are there in 200 years ? ā§¨ā§Ļā§Ļ āĻŦāĻā§°āĻ¤ āĻāĻŋāĻŽāĻžāĻ¨āĻāĻž Leap Year āĻĨāĻžāĻā§ ?
Soln
- 200 ÷ 4 = 50
- Century years are 100 and 200
- 100 and 200 are NOT divisible by 400
- So, both are not leap years
- Therefore, 2 leap years are reduced
Ans: 50 − 2 = 48 leap years
āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨ :
- 200 ÷ 4 = 50
- āĻļāĻ¤āĻŋāĻāĻž āĻŦāĻā§° = 100 āĻā§°ā§ 200
- āĻĻā§āĻ¯āĻŧā§āĻāĻž ā§Ēā§Ļā§Ļā§°ā§ āĻŦāĻŋāĻāĻžāĻā§āĻ¯ āĻ¨āĻšāĻ¯āĻŧ
- āĻ¸ā§āĻ¯āĻŧā§ ā§¨āĻāĻž Leap Year āĻŦāĻžāĻĻ
āĻāĻ¤ā§āĻ¤ā§°: 48āĻāĻž Leap Year
Q3. How many leap years are there in 300 years ? ā§Šā§Ļā§Ļ āĻŦāĻā§°āĻ¤ āĻāĻŋāĻŽāĻžāĻ¨āĻāĻž Leap Year āĻĨāĻžāĻā§ ?
Soln
- 300 ÷ 4 = 75
- Century years are 100, 200, 300
- None of them are divisible by 400
- Therefore, 3 leap years are reduced
Ans: 75 − 3 = 72 leap years
āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨:
- 300 ÷ 4 = 75
- āĻļāĻ¤āĻŋāĻāĻž āĻŦāĻā§° = 100, 200, 300
- āĻā§āĻ¨ā§āĻāĻž ā§Ēā§Ļā§Ļā§°ā§ āĻŦāĻŋāĻāĻžāĻā§āĻ¯ āĻ¨āĻšāĻ¯āĻŧ
- āĻ¸ā§āĻ¯āĻŧā§ ā§ŠāĻāĻž Leap Year āĻŦāĻžāĻĻ
āĻāĻ¤ā§āĻ¤ā§°: 72āĻāĻž Leap Year
Q4. How many leap years are there in 400 years ? ā§Ēā§Ļā§Ļ āĻŦāĻā§°āĻ¤ āĻāĻŋāĻŽāĻžāĻ¨āĻāĻž Leap Year āĻĨāĻžāĻā§ ?
Soln
- 400 ÷ 4 = 100
- Century years are 100, 200, 300, 400
- 100, 200, 300 are NOT leap years
- 400 IS divisible by 400, so it is a leap year
- Therefore, only 3 are reduced
Ans: 100 − 3 = 97 leap years
āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨:
- 400 ÷ 4 = 100
- āĻļāĻ¤āĻŋāĻāĻž āĻŦāĻā§° = 100, 200, 300, 400
- 100, 200, 300 Leap Year āĻ¨āĻšāĻ¯āĻŧ
- 400 Leap Year
- āĻ¸ā§āĻ¯āĻŧā§ ā§ŠāĻāĻž Leap Year āĻŦāĻžāĻĻ
āĻāĻ¤ā§āĻ¤ā§°: 97āĻāĻž Leap Year
Memory Points
- 100 years → 24 leap years : ā§§ā§Ļā§Ļ āĻŦāĻā§° → ā§¨ā§ĒāĻāĻž
- 200 years → 48 leap years : ā§¨ā§Ļā§Ļ āĻŦāĻā§° → ā§Ēā§ŽāĻāĻž
- 300 years → 72 leap years : ā§Šā§Ļā§Ļ āĻŦāĻā§° → ā§ā§¨āĻāĻž
- 400 years → 97 leap years : ā§Ēā§Ļā§Ļ āĻŦāĻā§° → ā§¯ā§āĻāĻž