The average age of a family having three members is 40 years. The smallest member of the family is 18 years old. The difference between the age of the oldest family member and the age of the second oldest family member is 6 more than the difference between the age of the second oldest member and age of youngest member of the family. Quantity I: 25 years hence, what will be the average of the age of smallest member and that of oldest member of the family? Quantity II: What is the age of the oldest member of the family?
The average age of a family having three members is 40 years. The smallest member of the family is 18 years old. The difference between the age of the oldest family member and the age of the second oldest family member is 6 more than the difference between the age of the second oldest member and age of youngest member of the family. Quantity I: 25 years hence, what will be the average of the age of smallest member and that of oldest member of the family? Quantity II: What is the age of the oldest member of the family? Correct Answer Quantity I > Quantity II
Let the ages of the oldest, second oldest and youngest family members be A, B and C respectively
According to the given information,
A + B + C = 40 × 3 = 120
⇒ A + B + C = 120 years
And,
∵ C = 18
⇒ A + B = 102 ---- (1)
Further,
∵ A – B = 6 + B – C
⇒ A – 2B = - 12 ---- (2)
From equation (1) and (2)
A = 64; B = 38
Quantity I: 25 years hence, Smallest Member’s age = 18 + 25 = 43 years
And Oldest member’s age = 64 + 25 = 89 years
Average = (43 + 89)/2 = 66
Quantity II: The age of oldest member of the family = A = 64 years
Therefore, Quantity I > Quantity II
Hence, option 3) is correct.