Question

The sum of all two digit numbers divisible by $5$ is:

• A. $1035$
• B. $1245$
• C. $1230$
• D. $945$
• E. None of these

Answer 1

The correct option is D $945$

Required numbers are $10,15,20,25,......96$
This is an A.P. in which $a=10,d=5$ and $l=95$
$t_n=95$ $\Rightarrow$ $a+(n-1)d=95$
$\Rightarrow$ $10+(n-1)\times 5=95$
$\Rightarrow$ $(n-1)\times 5=85$
$\Rightarrow$ $(n-1)=17$
$\Rightarrow$ $n=18$
$\therefore$ Required Sum $=\frac{n}{2}(a+l)=\frac{18}{2}\times (10+95)=(95\times 105)=945$