Multiple choice

$10$ years ago, the average age of a family of $4$ members was $24$ years. Two children having been born (with age difference of $2$ years), the present average age of the family is again $24$ years. Then the present age of the youngest child is:

  1. $1$ year
  2. $2$ years
  3. $3$ years
  4. $4$ years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

10 years ago: 4 members, average 24, sum = 96. Present sum = 96 + 4*10 = 136. Present family: 6 members, average 24, sum = 144. Sum of children = 144 - 136 = 8. Let children be x and x+2. x + x + 2 = 8 => 2x = 6 => x = 3.

AI explanation

Ten years ago, the total age of the 4 family members was 4 times 24, equaling 96 years. Today, the total age of those original 4 members is 96 plus 40, which equals 136 years. Since the present average age of the 6-member family remains 24, their current total age is 6 times 24, or 144 years. The combined age of the two children is 144 minus 136, equaling 8 years; since they are 2 years apart, the younger child is half of 8 minus 2, making the youngest child 3 years old.

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