Question

Find the no of times the 29th day of the moon occurs in 100 consecutive years

Answer 1

Let's start 29th day of this month as first term.

• In time period of 100 years, after each 4 year, there will be a leap year

• Number of leap years = 100/4 = 25 leap years.

______________________________

→ Total Number of days

= 75 × 365 + 25 × 366

= 36525 day

Out of this, 36511 is last term of A.P.

→ A.P = 29, 58, 87, ......, 36511

→ $\mathsf{a_n}$ = a + (n - 1)d

1. a = first term
2. ‘n’ = number of times
3. d = Comman difference
4. $\mathsf{a_n}$ = value of placing

______________________________

→ 36511 = a + (n - 1)d

→ 36511 = 29 + (n - 1)d

→ 36482 = (n - 1)29

→ 1258 = n - 1

→ 1258 + 1 = n

→ 1259 = n

Hence Full Moon will occur 1259 times on 29th day of Month in 100 consecutive years.

Answer : 1259

Answer 2

Answer

Leap comes once in every 4 years,

The 29th of each month comes for every year, so there are 4×100 = 400 29ths for all other months.

Example let this be

100/4 = 25 This is leap year

Number of days

75 × 365 + 25 × 366

Total number of days =36525

last term of =36511

29, 58, 87, and in 36511

term + number - 1 with its difference

Steps

⏭️36511 = term + number - 1{difference}

⏭️36511 = 29 + number - 1 {difference}

⏭️ 36482 = number - 1 with 29

⏭️1258 = number - 1

⏭️ 1258 + 1 = The number

⏭️ 1259 =The number

1259 times on 29th in 100 Moon comes

The total number of 29ths February in one month

This will be a 100 year may be 1259times!!!!!

Exactly =$(Answer=1259 times)$