Average age of a joint family over time

CAT 2007 Slot 1 · QA · Medium · Averages

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Ten years ago, the ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average age of this eight-member joint family is nearest to

  1. A.

    23 years

  2. B.

    22 years

  3. C.

    21 years

  4. D.

    25 years

  5. E.

    24 years

Answer

E

Explanation

Total age 10 years ago = 231. 3 years later (7 years ago): 231+8×3−60+0=195231 + 8 \times 3 - 60 + 0 = 195. 3 years later (4 years ago): 195+8×3−60+0=159195 + 8 \times 3 - 60 + 0 = 159. Current total age (4 years later): 159+8×4=191159 + 8 \times 4 = 191. Current average age =1918=23.875≈24= \frac{191}{8} = 23.875 \approx 24 years.

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