The average age of 9 sons in a family is 13 vears. The average age of mother, father and sons together is 20 years. If mother is 9 years younger than father. then what is the age of father?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 56 years.
Let the age of father be F, age of mother be M and age of each son be S.
Given that, average age of 9 sons = 13 years
Average age of mother father and 9 sons = 20 years
F - M = 9 ...(i)
Total age = Average age × Number of persons
According to the given question,
Total age of 9 sons = 9 × 13
⇒ 117 years
Total age of Father, mother and 9 sons = (F + M + 9S) = 11 × 20
⇒ 220 years
Age of (F + M) = 220 - 117
⇒ 103 years
Now, F - M = 9 ...(ii)
Adding equations (i) and (ii),
⇒ 2F = 112
⇒ F = 56 years
Hence the age of fathere is 56 years.