Q. 185.0( 3 Votes )

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


an = 99


A.P. is 12, 15,………,99


We know, an = 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 an = 99


Common difference, d1 = a2 – a1 = 15 – 12 = 3


Now, an = a1 + (n – 1)d


an = 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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