There are 17 persons in a group. The average age of 16 persons among t...
Let the average age of all the 17 persons = X years
Age of 17th persons = X + 8 years
16 × 60.50 + X + 8 = 17 × X
976 = 16X
X = 61
So the answer = 61 + 8 = 69 years
Hence, Option D is correct.
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There are 17 persons in a group. The average age of 16 persons among t...
Understanding the Problem
We have a group of 17 persons, where the average age of 16 persons is given as 60.50 years. We need to find the age of the 17th person, who is 8 years older than the average age of all 17 persons.
Step 1: Calculate the Total Age of 16 Persons
- Average age of 16 persons = 60.50 years
- Total age of 16 persons = Average age × Number of persons = 60.50 × 16 = 968 years
Step 2: Establish the Average Age of All 17 Persons
Let the average age of all 17 persons be "A".
- The total age of all 17 persons = Total age of 16 persons + Age of 17th person
- Therefore, Total age = 968 + Age of 17th person
Since the average age "A" can also be expressed as:
- A = Total age of all 17 persons ÷ 17
We can write:
A = (968 + Age of 17th person) / 17
Step 3: Age of the 17th Person
According to the problem, the age of the 17th person is 8 years more than the average age A:
- Age of 17th person = A + 8
Now, substituting this into our average equation gives:
A = (968 + (A + 8)) / 17
Simplifying this equation leads to finding the value of "A".
Step 4: Solve for A
Rearranging the equation:
17A = 968 + A + 8
- 16A = 976
- A = 61
Step 5: Calculate the Age of the 17th Person
The age of the 17th person = A + 8 = 61 + 8 = 69 years.
Conclusion
Thus, the age of the 17th person is 69 years. The correct answer is option 'D'.