Question

The sum of all odd numbers of four digits which are divisible by 9, is

• A. 2754000
• B. 2753000
• C. 2752000
• D. None of these

Answer 1

The correct option is A 2754000

The odd numbers of four digits which are divisible by 9 are 1017, 1035, . . . , 9999.
These are in AP with common difference 18.
Hence, nth term $=a{­}_n=a+(n-1)d$ Here, a = 1017 , d = 18 and l = 9999
$\therefore 9999=1017+(n-1)\times 18\Rightarrow 18n=9999-999=9000\Rightarrow N=500\Rightarrow S_n=\frac{n}{2}(a_1+a_n)=\frac{500}{2}(1017+9999)\therefore Sn=250\times 11016=2754000$