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

Question

How many numbers of two digit are divisible by $3$?

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Answer

Two digit numbers divisible by $3$
are, $12, 15, 18, ....., 99$
Hence, First term $a = 12$
Difference $d = 15 - 12 = 3$
and Last term $a_n = 99$
We know $n^{th}$ term of an $A.P.$
$a_n = a + (n - 1)d$
$\Rightarrow 99 = 12 + (n - 1)3$
$\Rightarrow 99 = 12 + 3n - 3$
$\Rightarrow 99 = 9 + 3n$
$\Rightarrow 90 = 3n$
$\Rightarrow n = 30$
Hence, Total number of two digit which one divisible by 3 is $30.$

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