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 of this eight-member joint family is nearest to

### Concept & Logic To find the current average age, we must track the total age of the family over time. The key principle is that for every passing year, the total age of the family increases by the number of living members. ### Step-by-Step Solution * **10 Years Ago ($T = -10$):** Family size = $8$. Total age = $231$. * **7 Years Ago ($T = -7$):** (3 years later) Total age increases by $8 \times 3 = 24$ years. Total age before changes = $231 + 24 = 255$. One member dies ($-60$) and a newborn is added ($+0$). New total age = $255 - 60 + 0 = 195$. (Family size remains $8$). * **4 Years Ago ($T = -4$):** (Another 3 years later) Total age increases by $8 \times 3 = 24$ years. Total age before changes = $195 + 24 = 219$. Another member dies ($-60$) and a newborn is added ($+0$). New total age = $219 - 60 + 0 = 159$. (Family size remains $8$). * **Present Day ($T = 0$):** (4 years later) Total age increases by $8 \times 4 = 32$ years. Current total age = $159 + 32 = 191$. Current average = $191 / 8 = 23.875$ years. ### Exam Strategy & Shortcut Instead of calculating the total age at every step, track the net change over the entire 10-year period. Because a birth instantly replaces every death, the family size is a constant $8$ people. Think of the family as $8$ "slots" that age continuously over the $10$ years. Total natural aging for these $8$ slots = $8 \times 10 = 80$ years. During this time, two people left the family, taking their accumulated ages with them at the exact time of their departure. Net Total Age = Initial Total + Total Natural Aging - Ages at Death Net Total = $231 + 80 - 60 - 60 = 191$. Current Average = $191 / 8 = 23.875$. This is nearest to $24$. This powerful logic bypasses tracking the individual newborns entirely and solves the problem in seconds! ### Common Pitfall Students often get tangled up trying to calculate the current ages of the newborns (who are $7$ and $4$ years old today). While calculating their specific individual ages works if you meticulously track every living member, it frequently leads to arithmetic errors and wastes valuable time. Leveraging the constant family size of $8$ to find the net total is much faster and safer. ### Final Answer **Therefore, the correct answer is 24 years.**