Three years ago the average age of a family of six members was 19 years. A boy have been born, the average age of the family is the same today. What is the age of the boy?A1 yearB1.5 yearC2 yearD2.5 year
Question
Three years ago the average age of a family of six members was 19 years. A boy have been born, the average age of the family is the same today. What is the age of the boy?A1 yearB1.5 yearC2 yearD2.5 year
Solution
To solve this problem, we need to understand that the average age of the family remains the same before and after the boy's birth. This means that the total age of the family members has increased exactly by the number of years that have passed, which is 3 years for each of the 6 original family members, so 18 years in total.
However, the family now has 7 members, so if the average age remained at 19 years, the total age of the family would be 7 * 19 = 133 years.
Three years ago, the total age of the family was 6 * 19 = 114 years. Over the course of 3 years, this total would naturally increase to 114 years + 18 years = 132 years.
So, the boy's age must be the difference between the current total age and the total age that would be expected naturally due to the passage of time, which is 133 years - 132 years = 1 year.
Therefore, the boy is 1 year old, so the answer is A.
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