Here you have to find

(i) the sum of two-digit whole numbers

(ii) which is divisible by 3

An Important question based on Arithmetic progression Chapter of R.S Aggarwal book for ICSE & CBSE Board.

This is the Question Number 7 Exercise 11 C of RS Aggarwal Solution.

a=1st two-digit number divisible by 3=12

a_n=last two-digit number divisible by 3=99

d=3

a_n=a+(n-1)d

99=12+(n-1)3

33=4+(n-1)3

29=(n-1)

n=30

S_n=(a+a_n)n/2

S_30=(12+99)15

S_30=111 x 15

S_30=1665

the sum of all two digits number which is divisible by 3 is 1665