Given: Natural numbers from 100 to 300 which are exactly divisible by 4 and 5.

To find: Sum of all such numbers.

Solution:

Step 1: Find the first number which satisfies the given condition.

The first natural number which is exactly divisible by both 4 and 5 is 20.

Step 2: Find the last number which satisfies the given condition.

The last natural number which is exactly divisible by both 4 and 5 and lies between 100 and 300 is 280.

Step 3: Find the common difference.

The common difference between consecutive terms in the given sequence is 20, as each term is obtained by adding 20 to the previous term.

Step 4: Find the number of terms.

The number of terms in the given sequence can be found by using the formula:

n = (last term - first term)/common difference + 1

n = (280 - 20)/20 + 1

n = 13

Step 5: Find the sum of the terms.

The sum of an arithmetic sequence can be found using the formula:

sum = n/2 × (first term + last term)

sum = 13/2 × (20 + 280)

sum = 143 × 300

sum = 42900

Therefore, the sum of all natural numbers from 100 to 300 which are exactly divisible by 4 and 5 is 42900.

However, this is not the final answer as we need to find the sum of only those numbers which are between 100 and 300. Let's modify our solution accordingly.

Step 6: Find the sum of the terms between 100 and 300.

We need to find the sum of the terms between 100 and 300, which are exactly divisible by 4 and 5. We can do this by finding the sum of the terms from 20 to 280 (which we already found in Step 5) and then subtracting the sum of the terms from 20 to 80 and from 300 to 280.

The sum of the terms from 20 to 80 can be found using the formula:

sum = n/2 × (first term + last term)

sum = 4/2 × (20 + 80)

sum = 200

The sum of the terms from 300 to 280 can be found using the formula:

sum = n/2 × (first term + last term)

sum = 11/2 × (280 + 300)

sum = 3080

Now, we can find the sum of the terms between 100 and 300 by subtracting the sum of the terms from 20 to 80 and from 300 to 280 from the sum of the terms from 20 to 280.

sum = 42900 - 200 - 3080

sum = 39820

Therefore, the sum of all natural numbers from 100 to 300 which are exactly divisible by 4 and 5 is 39820.

Hence, option (a) is the correct answer.