Question : The average age of 6 members of a family is 25 years. If the youngest member of the family is 15 years old, then what was the average age (in years) of the family at the time of the birth of the youngest member?
Option 1: 9
Option 2: 12
Option 3: 18
Option 4: 24
Correct Answer: 12
Solution :
Given that the average age of 6 members of a family is 25 years.
⇒ Sum of the age of 6 members of the family $=25\times6 = 150$
Youngest member of the family = 15 years
At the time of the birth of the youngest member, everyone would be 15 years younger and there will be five members only.
Now, sum of 5 members = Sum of ages 6 members – (6 × 15) = 150 – 90 = 60
$\therefore$ Required Average $=\frac{\text{Sum of age of 5 members}}{5}=\frac{60}{5} = 12$ years
Hence, the correct answer is 12.
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