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9 years ago, the average age of a family of five members was 33 years. Now, three new members join whose ages are in ascending order with consecutive gaps of 8 years. If the present average age of the family is the same as it was 9 years ago, what is the age (in years) of the youngest new member?

9 years ago, the average age of a family of five members was 33 years. Now, three new members join whose ages are in ascending order with consecutive gaps of 8 years. If the present average age of the family is the same as it was 9 years ago, what is the age (in years) of the youngest new member? Correct Answer 10

The age of the family 9 years ago = 5 × 33 = 165

The age of the family at present = 165 + 5 × 9 = 210

Let the ages of three new members of the family are a, (a + 8) and (a + 16).

According to the question,

Present average age of the family = 33

⇒ /8 = 33

⇒ 210 + 3a + 24 = 264

⇒ 3a = 30

⇒ a = 10 years.

∴ the age of the youngest member = 10 years.

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