Three years ago, the average age of a family of 5 members was 17 years. A baby having been born, the average age of the family is the same today. The present age of the baby is:Options :2 years2.4 years3 years1.5 years
Question
Three years ago, the average age of a family of 5 members was 17 years. A baby having been born, the average age of the family is the same today. The present age of the baby is:Options :2 years2.4 years3 years1.5 years
Solution
To solve this problem, we need to understand that the average age of the family remains the same before and after the baby is born. This means that the total age of the family members (excluding the baby) has increased by the same amount as the baby's current age over the three years.
Step 1: Calculate the total age of the family three years ago. Since the average age was 17 and there were 5 members, the total age was 17 * 5 = 85 years.
Step 2: Calculate the total age of the family now, excluding the baby. Since the average age is still 17 and there are now 6 members, the total age is 17 * 6 = 102 years.
Step 3: Subtract the total age three years ago from the total age now to find the increase. This is 102 - 85 = 17 years.
Step 4: Since this increase over three years is due to the aging of the 5 original family members and the baby's age, and we know that each of the original members has aged 3 years, we subtract the aging of the original members from the total increase. This is 17 - (5 * 3) = 2 years.
So, the baby is 2 years old.
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