### Theory:

Consider the following situation one by one.
Example:
1. Malar scored $$10$$ marks higher than Prem in Mathematics. Will you be able to find Prem's marks in mathematics if you know Malar's marks.

Yes, It is possible to find Prem's mark.

Since Malar's mark is not  mentioned explicitly, we can take the Malar's mark as $$n$$.

We know that 'Malar scored $$10$$ marks higher than Prem '.

So Prem's mark should be $$10$$ less than Malar's mark.

Thus, Prem's mark becomes $$n-10$$.

Let us verify this problem:

Suppose Malar's mark is $$90$$. Then Prem's mark becomes $$n-10 = 90 - 10 = 80$$.

It says that Malar's mark (90) is $$10$$ higher than Prem's mark (80).

Thus, our rule is correct.

2. Ezhil is $$5$$ years younger than his sister Kavitha. Is it possible to find Ezhil's age if we know Kavitha's age?

Here Ezhil is $$5$$ years younger than his sister Kavitha. And Kavitha's age is known to us.

Let Kavitha's age be $$k$$.

We know that 'Ezhil is $$5$$ years younger than his sister Kavitha'.

So Ezhil's age should be $$5$$ less than Kavitha's age.

Thus, Ezhils present age $$k-5$$.

Let us verify this problem:

Suppose Kavitha's age is $$30$$. Then Ezhil's age is $$k-5 = 30 - 5 = 25$$.

It says that Ezhil (25) is $$5$$ years younger than Kavitha $$(30)$$.

Thus, our rule is correct.

3. Kamal's present age is $$a$$. Is it  possible to express Kamal's age after $$8$$ years in terms of $$a$$?

Given that Kamal's present age is $$a$$ and we have to express Kamal's age after $$8$$ years.

After $$8$$ years, Kamal will be $$8$$ years older than now. So we have to add $$8$$ to this present age.

Thus, Kamal's age after $$8$$ years is $$a+8$$.

4. Complete the sequence.

 $$5$$ $$9$$ $$14$$ $$20$$ $$27$$ ___

Note that each element in the sequence increases a certain number than the previous element.

Let us look for the pattern.

Here the first number is $$5$$ and the second number is $$9$$. Added the number $$4$$ to $$5$$ to get $$5+4 = 9$$.

Here the third number is $$14$$. Added $$5$$ to the previous number $$9$$ to get $$9+5 = 14$$.

Here the fourth number is $$20$$. Added $$6$$ to the previous number $$14$$ to get $$14+6 = 20$$.

Here the fifth number is $$27$$. Added $$7$$ to the previous number $$20$$ to get $$20+7 = 27$$.

In the same pattern, we can find the sixth number.

The next number will be the result of adding the previous number with $$8$$.

That is, the sixth number is adding $$8$$ to the previous number $$27$$.

$$8+27 = 35$$

Therefore, the sixth number is $$35$$.