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There are 17 persons in a group. The average age of 16 persons among them is 60.50 years and the age of 17th person is 8 years more than the average age of all the 17 persons. What is the age of the 17th person?
- a)54 years
- b)64 years
- c)60 years
- d)69 years
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
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.
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.
Most Upvoted Answer
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'.
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'.
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There are 17 persons in a group. The average age of 16 persons among them is 60.50 years and the age of 17th person is 8 years more than the average age of all the 17 persons. What is the age of the 17th person?a)54 yearsb)64 yearsc)60 yearsd)69 yearsCorrect answer is option 'D'. Can you explain this answer?
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