CAT 2007 — QA Question 24
Answer the next 2 questions based on the information given below.
Let a1 = p and b1 = q, where p and q are positive quantities.
Define:
an = pbn−1 bn = qbn−1, for even n > 1 and
an = pan − 1 bn = qan − 1, for odd n > 1.
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:
Answer & solution
- A
23 years
- B
22 years
- C
21 years
- D
25 years
24 years
The sum of the ages of the members of the family ten years ago = 231
∴ The sum of the ages of 8 (including the newborn) members of the family seven years ago = 231 + (3 × 8) – 60 = 195
∴ The sum of the ages of 8 (including the newborn) members of the family four years ago = 195 + (3 × 8) – 60 = 159
∴ The sum of the ages of 8 members of the family now = 159 + (4 × 8) = 191
∴ Required average = 191/8 = 23.875 ≈ 24
Hence, option (e).