daniel18vap wrote:
Average age of a family of 5 members at present is 35. If After some years, the eldest member of the family will die, and twins are born just one year before death, such that 6 years after death, the average age of family will become 25.5 years. If the eldest member will die at the age of 85 years, find after how many years from present, will he die?
A 10 years
B 2 years
C 5 years
D 15 years
E 12 years
Solution
• At present:
o Average age of the family \(= \frac{The\space sum \space of \space ages\space of \space all \space5 \space family \space members}{5 }= 35\)
\(⟹ The\space sum \space of \space ages\space of \space all \space5 \space family \space members = 35*5 = 175\)
• Let us assume that the eldest member of the family die after x years from present.
• Just before the death of the eldest member of the family:
o The number of family members \(= 7\)
o The sum of ages of 5 members of the family(except twins) \(= 175 + 5x\)
o The sum of the ages of the twins \(= 2*1\)
o Total age of the family \(= (175 + 5x + 2)= (177 +5x)\)
• 6 years after the death:
o The total number of family members \(= 7 -1 =6\)
o And their total ages \(= (177 + 5x) – 85 + 6*6 = 128 +5x\)
o Average age of the family \(= \frac{128 +5x }{6} = 25.5\)
\(⟹128 + 5x = 153\)
\(⟹5x = 25 \)
\(⟹ x = 5\)
Thus, the correct answer is
Option C.