How many two-digit numbers are divisible by 3?

The two-digit numbers divisible by 3 are 12, 15, 18, ..., 99.

Clearly, these number are in AP.

Here, a = 12 and d = 15 − 12 = 3

Let this AP contains n terms. Then,

$a_{n}=99$

$\Rightarrow 12+(n-1) \times 3=99 \quad\left[a_{n}=a+(n-1) d\right]$

$\Rightarrow 3 n+9=99$

$\Rightarrow 3 n=99-9=90$

$\Rightarrow n=30$

Hence, there are 30 two-digit numbers divisible by 3.