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The average age of my family including me is 26.5 years and the average age of my family excluding me is 32 years. My family includes my parents and my sibling(s). It is also known that the age difference between two pairs of members is 2 and 4 years and ages of all family members are natural numbers. Which of the following is a possible age of my father?
- a)40
- b)42
- c)46
- d)Options 1, 2 and 3
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The average age of my family including me is 26.5 years and the averag...
Solution: Let the number of family members in my family excluding me be n.
My age = 26.5(n + 1) - 32n = 26.5 - 5.5n The possible values that n can take are 1 and 3 ( All ages are natural numbers).
However, 1 is not possible as there are parents and siblings in the family. n = 3, so there are 4 members in the family.
Also, my age = 26.5 - 5.5 * 3 = 10 years and total age of all the family members = 26.5 * 4 = 106 years
As it is given that there is an age difference of 2 and 4 years between 2 pairs of family members, the 2 pairs are the mother, father and the two siblings.
Let the age of my father be x.
My age = 26.5(n + 1) - 32n = 26.5 - 5.5n The possible values that n can take are 1 and 3 ( All ages are natural numbers).
However, 1 is not possible as there are parents and siblings in the family. n = 3, so there are 4 members in the family.
Also, my age = 26.5 - 5.5 * 3 = 10 years and total age of all the family members = 26.5 * 4 = 106 years
As it is given that there is an age difference of 2 and 4 years between 2 pairs of family members, the 2 pairs are the mother, father and the two siblings.
Let the age of my father be x.
Case 1: (x)+ (x + 4) + (10) + (10 + 2) = 106 x = 40
Case 2: (x)+ (x + 4) + (10) + (10 - 2) = 106 x = 42
Case 3: (x)+ ( x - 4) + (10) + (10 + 2) = 106 x = 44
Case 4: (x)+ ( x - 4) + (10) + (10 - 2) = 106 x = 46
Case 5: (x)+ (x + 2) + (10) + (10 + 4) = 106 x = 40
Case 6: (x)+ (x + 2) + (10) + (10 - 4) = 106 x = 44
Case 7: (x)+ (x - 2) + (10) + (10 + 4) = 106 x = 42
Case 8:(x)+ ( x - 2 ) + (1 0 ) + (1 0 - 4 ) = 106 x = 46
The age of my father can be 40, 42, 44 and 46 Hence, option 4.
The age of my father can be 40, 42, 44 and 46 Hence, option 4.
Most Upvoted Answer
The average age of my family including me is 26.5 years and the averag...
Solution:
Let the ages of my father, mother, and sibling(s) be F, M, and S respectively.
Given:
Average age of my family including me = 26.5 years
∴ (F + M + S + my age) / (4) = 26.5
F + M + S + my age = 106 --- (1)
Average age of my family excluding me = 32 years
∴ (F + M + S) / (3) = 32
F + M + S = 96 --- (2)
Age difference between two pairs of members is 2 and 4 years.
There are three possible cases:
Case 1: F - M = 2 and M - S = 4
Adding these two equations, we get:
F - S = 6 --- (3)
Substituting equation (3) in equation (2), we get:
2M + 6 = 96
M = 45 (not a natural number)
Hence, this case is not possible.
Case 2: F - M = 4 and M - S = 2
Adding these two equations, we get:
F - S = 6 --- (4)
Substituting equation (4) in equation (2), we get:
2M + 6 = 96
M = 45 (not a natural number)
Hence, this case is also not possible.
Case 3: F - S = 2 and M - S = 4
Adding these two equations, we get:
F - M = -2 --- (5)
Substituting equation (5) in equation (2), we get:
2S + F = 96
Substituting equation (2) in equation (1), we get:
F + M + S + my age = 106
Substituting M + S = 96 - F from equation (2), we get:
F + 96 - F + my age = 106
my age = 10 (a natural number)
Hence, the possible age of my father is F = 40, which is option (d).
Therefore, the correct answer is option (d).
Let the ages of my father, mother, and sibling(s) be F, M, and S respectively.
Given:
Average age of my family including me = 26.5 years
∴ (F + M + S + my age) / (4) = 26.5
F + M + S + my age = 106 --- (1)
Average age of my family excluding me = 32 years
∴ (F + M + S) / (3) = 32
F + M + S = 96 --- (2)
Age difference between two pairs of members is 2 and 4 years.
There are three possible cases:
Case 1: F - M = 2 and M - S = 4
Adding these two equations, we get:
F - S = 6 --- (3)
Substituting equation (3) in equation (2), we get:
2M + 6 = 96
M = 45 (not a natural number)
Hence, this case is not possible.
Case 2: F - M = 4 and M - S = 2
Adding these two equations, we get:
F - S = 6 --- (4)
Substituting equation (4) in equation (2), we get:
2M + 6 = 96
M = 45 (not a natural number)
Hence, this case is also not possible.
Case 3: F - S = 2 and M - S = 4
Adding these two equations, we get:
F - M = -2 --- (5)
Substituting equation (5) in equation (2), we get:
2S + F = 96
Substituting equation (2) in equation (1), we get:
F + M + S + my age = 106
Substituting M + S = 96 - F from equation (2), we get:
F + 96 - F + my age = 106
my age = 10 (a natural number)
Hence, the possible age of my father is F = 40, which is option (d).
Therefore, the correct answer is option (d).
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The average age of my family including me is 26.5 years and the average age of my family excluding me is 32 years. My family includes my parents and my sibling(s). It is also known that the age difference between two pairs of members is 2 and 4 years and ages of all family members are natural numbers. Which of the following is a possible age of my father?a)40b)42c)46d)Options 1, 2 and 3Correct answer is option 'D'. Can you explain this answer?
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