There are 30 two-digit numbers divisible by 3.
This can be solved using the concept of arithmetic progression (AP). The two-digit numbers divisible by 3 form an arithmetic sequence: 12, 15, 18, ..., 99.
- First term (a): 12
- Common difference (d): 3
- Last term (l): 99
We can use the formula for the nth term of an AP: l = a + (n-1)d, where 'n' is the number of terms.
Solving for 'n':
99 = 12 + (n-1)3
87 = (n-1)3
29 = n-1
n = 30
Therefore, there are 30 two-digit numbers divisible by 3. Multiple sources (Byjus, Shaalaa, Doubtnut, Teachoo, LearnAtNoon, Unacademy) confirm this result.
