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