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The average age of a family of five members is 24. If the present age of the youngest member is 8 years, what was the average age of the family at the time of the birth of the youngest member?
- a)20 years
- b)16 years
- c)12 years
- d)18 years
- e)21 years
Correct answer is option 'A'. Can you explain this answer?
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The average age of a family of five members is 24. If the present age ...
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The average age of a family of five members is 24. If the present age ...
Given data:
- Average age of a family of five members = 24
- Present age of the youngest member = 8 years
To find: Average age of the family at the time of the birth of the youngest member
Solution:
Let the present age of the other four members be a, b, c, and d.
Then, the sum of their present ages = a + b + c + d
And, the sum of their ages at the time of the birth of the youngest member = a + b + c + d + 8 (as the youngest member was not born at that time)
As we know, the average age of a group is the sum of their ages divided by the number of members in the group.
So, we have:
- Average age of the family at present = (a + b + c + d + 8)/5
- Average age of the family at the time of the birth of the youngest member = (a + b + c + d)/5
We can find the value of (a + b + c + d) by using the fact that the average age of the family at present is 24. So, we have:
(a + b + c + d + 8)/5 = 24
=> a + b + c + d + 8 = 120
=> a + b + c + d = 112
Substituting this value in the equation for the average age at the time of the birth of the youngest member, we get:
Average age of the family at the time of the birth of the youngest member = (a + b + c + d)/5
= 112/5
= 22.4
Therefore, the average age of the family at the time of the birth of the youngest member was 22.4. But this is not one of the given options. So, we need to round off the value to the nearest integer, which is 22. And, option (a) says 20, which is not the correct answer. So, the given answer key is incorrect.
- Average age of a family of five members = 24
- Present age of the youngest member = 8 years
To find: Average age of the family at the time of the birth of the youngest member
Solution:
Let the present age of the other four members be a, b, c, and d.
Then, the sum of their present ages = a + b + c + d
And, the sum of their ages at the time of the birth of the youngest member = a + b + c + d + 8 (as the youngest member was not born at that time)
As we know, the average age of a group is the sum of their ages divided by the number of members in the group.
So, we have:
- Average age of the family at present = (a + b + c + d + 8)/5
- Average age of the family at the time of the birth of the youngest member = (a + b + c + d)/5
We can find the value of (a + b + c + d) by using the fact that the average age of the family at present is 24. So, we have:
(a + b + c + d + 8)/5 = 24
=> a + b + c + d + 8 = 120
=> a + b + c + d = 112
Substituting this value in the equation for the average age at the time of the birth of the youngest member, we get:
Average age of the family at the time of the birth of the youngest member = (a + b + c + d)/5
= 112/5
= 22.4
Therefore, the average age of the family at the time of the birth of the youngest member was 22.4. But this is not one of the given options. So, we need to round off the value to the nearest integer, which is 22. And, option (a) says 20, which is not the correct answer. So, the given answer key is incorrect.
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The average age of a family of five members is 24. If the present age of the youngest member is 8 years, what was the average age of the family at the time of the birth of the youngest member?a)20 yearsb)16 yearsc)12 yearsd)18 yearse)21 yearsCorrect answer is option 'A'. Can you explain this answer?
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