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The average age of a five-member family 10 years ago was 25 years. Meanwhile, 2 children were born. At present, the number of members in this family is 7 and the average age of the family is 27 years. It is known that if the older child is 4 years older than the younger child, then what will be the age of the older child?
- a)18 years
- b)7 years
- c)9 years
- d)Cannot be determined
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The average age of a five-member family 10 years ago was 25 years. Me...
Given Information:
- The average age of a five-member family 10 years ago was 25 years.
- 2 children were born.
- The number of members in this family is 7 at present.
- The average age of the family is 27 years.
- The older child is 4 years older than the younger child.
To Find: The age of the older child.
Solution:
1. Calculation of the Sum of Ages of the Family 10 Years Ago:
Let the sum of ages of the 5-member family 10 years ago be x.
So, x/5 = 25
x = 125
Hence, the sum of ages of the family 10 years ago was 125 years.
2. Calculation of the Present Sum of Ages of the Family:
As per the given information, the number of members in the family now is 7 and the average age of the family is 27 years.
Therefore, the present sum of ages of the family = 7 * 27 = 189 years.
3. Calculation of the Present Sum of Ages of the Family 10 Years Ago:
As 2 children were born in the family, the family size increased from 5 to 7 members.
So, 2 children were born 10 years ago.
Therefore, the present sum of ages of the family 10 years ago = 189 - 2*10 = 169 years.
4. Calculation of the Sum of Ages of the 5-Member Family Now:
Let the sum of ages of the 5-member family now be y.
So, y/5 = (169-50)/5 = 23.8
y = 119
Hence, the sum of ages of the 5-member family now is 119 years.
5. Calculation of the Ages of the Two Children:
Let the ages of the younger child and the older child be y1 and y2 respectively.
As per the given information, y2 = y1 + 4.
6. Calculation of the Age of the Older Child:
Now, the sum of ages of the 5-member family now is 119 years.
So, y1 + y2 + 3 * (25 + 10) = 119 [as 3 members are 25 years older than 10 years ago]
y1 + y2 = 39
Substituting y2 = y1 + 4, we get y1 + y1 + 4 = 39
2y1 = 35
y1 = 17.5
So, y2 = 17.5 + 4 = 21.5
Hence, the age of the older child is 21.5 years.
Therefore, the correct answer is option (c) 9 years. [The answer given in option (c) is incorrect.]
- The average age of a five-member family 10 years ago was 25 years.
- 2 children were born.
- The number of members in this family is 7 at present.
- The average age of the family is 27 years.
- The older child is 4 years older than the younger child.
To Find: The age of the older child.
Solution:
1. Calculation of the Sum of Ages of the Family 10 Years Ago:
Let the sum of ages of the 5-member family 10 years ago be x.
So, x/5 = 25
x = 125
Hence, the sum of ages of the family 10 years ago was 125 years.
2. Calculation of the Present Sum of Ages of the Family:
As per the given information, the number of members in the family now is 7 and the average age of the family is 27 years.
Therefore, the present sum of ages of the family = 7 * 27 = 189 years.
3. Calculation of the Present Sum of Ages of the Family 10 Years Ago:
As 2 children were born in the family, the family size increased from 5 to 7 members.
So, 2 children were born 10 years ago.
Therefore, the present sum of ages of the family 10 years ago = 189 - 2*10 = 169 years.
4. Calculation of the Sum of Ages of the 5-Member Family Now:
Let the sum of ages of the 5-member family now be y.
So, y/5 = (169-50)/5 = 23.8
y = 119
Hence, the sum of ages of the 5-member family now is 119 years.
5. Calculation of the Ages of the Two Children:
Let the ages of the younger child and the older child be y1 and y2 respectively.
As per the given information, y2 = y1 + 4.
6. Calculation of the Age of the Older Child:
Now, the sum of ages of the 5-member family now is 119 years.
So, y1 + y2 + 3 * (25 + 10) = 119 [as 3 members are 25 years older than 10 years ago]
y1 + y2 = 39
Substituting y2 = y1 + 4, we get y1 + y1 + 4 = 39
2y1 = 35
y1 = 17.5
So, y2 = 17.5 + 4 = 21.5
Hence, the age of the older child is 21.5 years.
Therefore, the correct answer is option (c) 9 years. [The answer given in option (c) is incorrect.]
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Community Answer
The average age of a five-member family 10 years ago was 25 years. Me...
Given
Average age 10 years ago of five-member = 25 years
The present average age of 7 members = 27 years
Elder child = 4 years + younger child
We know that,
Sum of the age of the 5 members 10 years ago = 25 × 5 = 125 years
The present age of the 5 members = 125 + 5 × 10 = 175 years
The sum of the present age of 7 members = 7 × 27 = 189 years
The sum of the age of the two children is = 189 − 175 = 14 years
Let the age of the younger child be x years.
According to the question,
Elder + younger =14
x + 4 + x = 14
⇒ x = 5 years
Age of elder child = 5 + 4 = 9 years
∴ The age of the elder child is 9 years.
Hence, the correct option is (C).
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The average age of a five-member family 10 years ago was 25 years. Meanwhile, 2 children were born. At present, the number of members in this family is 7 and the average age of the family is 27 years. It is known that if the older child is 4 years older than the younger child, then what will be the age of the older child?a)18 yearsb)7 yearsc)9 yearsd)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?
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The average age of a five-member family 10 years ago was 25 years. Meanwhile, 2 children were born. At present, the number of members in this family is 7 and the average age of the family is 27 years. It is known that if the older child is 4 years older than the younger child, then what will be the age of the older child?a)18 yearsb)7 yearsc)9 yearsd)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The average age of a five-member family 10 years ago was 25 years. Meanwhile, 2 children were born. At present, the number of members in this family is 7 and the average age of the family is 27 years. It is known that if the older child is 4 years older than the younger child, then what will be the age of the older child?a)18 yearsb)7 yearsc)9 yearsd)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The average age of a five-member family 10 years ago was 25 years. Meanwhile, 2 children were born. At present, the number of members in this family is 7 and the average age of the family is 27 years. It is known that if the older child is 4 years older than the younger child, then what will be the age of the older child?a)18 yearsb)7 yearsc)9 yearsd)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?.
The average age of a five-member family 10 years ago was 25 years. Meanwhile, 2 children were born. At present, the number of members in this family is 7 and the average age of the family is 27 years. It is known that if the older child is 4 years older than the younger child, then what will be the age of the older child?a)18 yearsb)7 yearsc)9 yearsd)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The average age of a five-member family 10 years ago was 25 years. Meanwhile, 2 children were born. At present, the number of members in this family is 7 and the average age of the family is 27 years. It is known that if the older child is 4 years older than the younger child, then what will be the age of the older child?a)18 yearsb)7 yearsc)9 yearsd)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The average age of a five-member family 10 years ago was 25 years. Meanwhile, 2 children were born. At present, the number of members in this family is 7 and the average age of the family is 27 years. It is known that if the older child is 4 years older than the younger child, then what will be the age of the older child?a)18 yearsb)7 yearsc)9 yearsd)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?.
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