How many two digit numbers are divisible by 3? - Vidyadip

Question

How many two digit numbers are divisible by 3?

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Answer

Two digits numbers divisible by 3 are
$
12,15,18,21, \ldots, 99
$
Here, $a=13, d=15-12=3$ and $I =99$
Let number divisible by 3 and $n$
$
\begin{aligned}
& \therefore T_n=1=a+(n-1) d \\
& 99=12+(n-1) \times 3 \\
& \Rightarrow 99-12=3(n-1) \\
& \Rightarrow 3(n-1)=87 \\
& \Rightarrow n-1=\frac{87}{3}=29 \\
& \therefore n=29+1 \\
& =30 .
\end{aligned}
$

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