Question : What is the sum of all three digits numbers which are divisible by 20?
Option 1: 21400
Option 2: 24300
Option 3: 25800
Option 4: 22500
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Correct Answer: 24300
Solution :
The first three-digit number divisible by 20 is 100 and the last is 980
This forms an arithmetic series with first term ($a$) = 100, common difference ($d$) = 20 and last term ($l$) = 980
⇒ The sum of an arithmetic series = $\frac{n}{2} × (a + l)$, where $n$ is the number of terms
We know, $n = \frac{l - a}{d} + 1$
⇒ $n=\frac{980-100}{20}+1$
⇒ $n=\frac{880}{20}+1$
⇒ $n=44+1=45$
So, the sum $=\frac{45}{2} × (100 + 980)= 24300$
Hence, the correct answer is 24300.
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