How many numbers of two digit are divisible by 3?

1.	How many numbers of two digit are divisible by 3?
Answer» For finding total two-digit numbers which are divisible by 3, Firstly we will make an A.P. of those two-digit numbers which are divisible by 3. First two digit number which is divisible by 3 is 12 ∴ a₁ = a = 12 Next two digit number which is divisible by 3 is 15 ∴ a₂ = 15 Largest two digit number which is divisible by 3 is 99 ∴ a_n = 99 ⇒ A.P. is 12, 15,………,99 We know, a_n= a + (n – 1)d Where a is first term or a and d is common difference and n is any natural number ⇒ a₁ = 12, a₂ = 15 and a_n = 99 Common difference, d₁ = a₂ – a₁ = 15 – 12 = 3 Now, a_n = a₁ + (n – 1)d ⇒ a_n = 12 + (n – 1)3 ⇒ 99 = 12 + 3n – 3 ⇒ 99 = 3n + 9 ⇒ 99 – 9 = 3n ⇒ 90 = 3n ⇒ n = 30 Hence, There are total 30 two-digit numbers which are divisible by 3.

Answer»

For finding total two-digit numbers which are divisible by 3,

Firstly we will make an A.P. of those two-digit numbers which are divisible by 3.

First two digit number which is divisible by 3 is 12

∴ a₁ = a = 12

Next two digit number which is divisible by 3 is 15

∴ a₂ = 15

Largest two digit number which is divisible by 3 is 99

∴ a_n = 99

⇒ A.P. is 12, 15,………,99

We know,

a_n= a + (n – 1)d

Where a is first term or a and d is common difference and n is any natural number

⇒ a₁ = 12, a₂ = 15 and a_n = 99

Common difference,

d₁ = a₂ – a₁

= 15 – 12

= 3

Now,

a_n = a₁ + (n – 1)d

⇒ a_n = 12 + (n – 1)3

⇒ 99 = 12 + 3n – 3

⇒ 99 = 3n + 9

⇒ 99 – 9 = 3n

⇒ 90 = 3n

⇒ n = 30

Hence,

There are total 30 two-digit numbers which are divisible by 3.

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