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The average age of a man and his son is 33 years. The ratio of their ages is 8 : 3 respectively. What is the man's age?
- a)48 years
- b)44 years
- c)42 years
- d)50 years
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The average age of a man and his son is 33 years. The ratio of their a...
Total age of the father and the son
= 2 x 33
= 66 years
Ratio in Father's age and son's age
= 8 : 3
∴ Father's age = 8 x 66/8 + 3
= 48 years
= 2 x 33
= 66 years
Ratio in Father's age and son's age
= 8 : 3
∴ Father's age = 8 x 66/8 + 3
= 48 years
Most Upvoted Answer
The average age of a man and his son is 33 years. The ratio of their a...
Understanding the Problem
The problem states that the average age of a man and his son is 33 years and their ages are in the ratio of 8:3. We need to find the man's age.
Calculating the Total Age
- The average age is given as 33 years.
- Since the average is calculated as (sum of ages) / 2, we can find the total age.
- Total age of the man and his son = 33 * 2 = 66 years.
Using the Age Ratio
- The ratio of their ages is 8:3.
- This means if we let the man's age be 8x and the son's age be 3x, then we can express their total age as:
- 8x + 3x = 11x.
Setting Up the Equation
- We know from the total age calculation that:
- 11x = 66 years.
Solving for x
- Now, divide both sides by 11:
- x = 66 / 11 = 6.
Finding Individual Ages
- Substitute x back to find their ages:
- Man's age = 8x = 8 * 6 = 48 years.
- Son's age = 3x = 3 * 6 = 18 years.
Conclusion
- The man is 48 years old, confirming that the correct answer is option 'A'.
The problem states that the average age of a man and his son is 33 years and their ages are in the ratio of 8:3. We need to find the man's age.
Calculating the Total Age
- The average age is given as 33 years.
- Since the average is calculated as (sum of ages) / 2, we can find the total age.
- Total age of the man and his son = 33 * 2 = 66 years.
Using the Age Ratio
- The ratio of their ages is 8:3.
- This means if we let the man's age be 8x and the son's age be 3x, then we can express their total age as:
- 8x + 3x = 11x.
Setting Up the Equation
- We know from the total age calculation that:
- 11x = 66 years.
Solving for x
- Now, divide both sides by 11:
- x = 66 / 11 = 6.
Finding Individual Ages
- Substitute x back to find their ages:
- Man's age = 8x = 8 * 6 = 48 years.
- Son's age = 3x = 3 * 6 = 18 years.
Conclusion
- The man is 48 years old, confirming that the correct answer is option 'A'.
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The average age of a man and his son is 33 years. The ratio of their ages is 8 : 3 respectively. What is the mans age?a)48 yearsb)44 yearsc)42 yearsd)50 yearsCorrect answer is option 'A'. Can you explain this answer?
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