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

Options

A. 24 years
B. 23 years
C. 22 years
D. 21 years

Answer

To solve the problem step by step, we will follow the chronological events and calculations as described in the question.

### Step 1: Determine the total age of the family 10 years ago.
The problem states that ten years ago, the ages of the eight family members added up to 231 years.
- **Total age 10 years ago = 231 years**

### Step 2: Calculate the total age of the family 7 years ago.
Three years after the initial 10 years ago (which is now 7 years ago), each of the eight members would have aged 3 years. Therefore, we add 3 years for each of the 8 members:
- **Total age 7 years ago = 231 + (3 * 8) = 231 + 24 = 255 years**

Next, one member died at the age of 60, so we subtract 60 from the total:
- **Total age 7 years ago after one member died = 255 - 60 = 195 years**

### Step 3: Calculate the total age of the family 4 years ago.
Now, three more years later (which is 4 years ago), again each of the remaining 7 members aged 3 years:
- **Total age 4 years ago = 195 + (3 * 7) = 195 + 21 = 216 years**

Then, again, one member died at the age of 60, and a child was born, so we subtract 60 and add 0 (for the newborn):
- **Total age 4 years ago after another member died = 216 - 60 = 156 years**

### Step 4: Calculate the total age of the family currently.
Now, we need to find the current total age, which is 4 years after the previous calculation:
- **Total age now = 156 + (4 * 8) = 156 + 32 = 188 years**

### Step 5: Calculate the current average age.
To find the average age of the family now, we divide the total age by the number of family members:
- **Average age = Total age now / Number of members = 188 / 8 = 23.5 years**

### Step 6: Round to the nearest whole number.
Since the question asks for the nearest whole number:
- **Rounded average age = 24 years**

### Conclusion:
The current average age of the eight-member joint family is approximately **24 years**.

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