Question : What is the sum of all two-digit numbers which are divisible by 9?
Option 1: 565
Option 2: 535
Option 3: 585
Option 4: 475
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Correct Answer: 585
Solution :
Sum of an arithmetic series = $\frac{n}{2} × (\text{first term + last term})$
⇒ Two digit numbers divisible by 9: 18, 27, 36,..., 99 (Total terms = 10)
So, the sum = $\frac{10}{2} × (18 + 99) = 585$
Therefore, the sum of all two-digit numbers which are divisible by 9 is 585.
Hence, the correct answer is 585.
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