Q. 185.0( 4 Votes )

# How many numbers

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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