Answer the questions independently of each other.The average age of members in my family excluding me is 27 years but including me is 22.25 years. If my family includes only myself, my parents and my siblings and there are two different pairs of members whose ages differ by 3 years and 4 years, then which of the following can be the age of any one member of my family? (All the ages are natural numbers)36 years34 years25 years35 years

The problem can be solved by using the concept of averages.

Step 1: Calculate the total age of all family members excluding you.

The average age of the family members excluding you is 27 years. If we assume that there are 'n' members in the family excluding you, then the total age of all these members is 27n.

Step 2: Calculate the total age of all family members including you.

The average age of the family members including you is 22.25 years. Since you are included in this, the total number of family members is 'n+1'. Therefore, the total age of all these members is 22.25(n+1).

Step 3: Find your age.

Since the total age of all members including you is greater than the total age of all members excluding you, the difference between these two amounts will give your age.

So, your age = 22.25(n+1) - 27n = 22.25n + 22.25 - 27n = 22.25 - 4.75n.

Step 4: Since your age must be a natural number, 'n' must be such that 4.75n is a natural number. The smallest such 'n' is 4.

So, your age = 22.25 - 4.75*4 = 4.25, which is not a natural number. Therefore, there is no solution to this problem based on the given conditions.

Therefore, none of the given ages can be the age of any one member of the family.