Age Problems
Question 1:
The sum of the present ages of A and B is 64. Five years ago, the ratio of their ages was 3:2. Find their present ages.
Solution:
Let the present age of A be 3x and B be 2x.
According to the given information, 3x + 2x = 64.
Simplifying the equation, 5x = 64.
Dividing both sides by 5, we get x = 12.8.
Therefore, the present age of A = 3x = 3 * 12.8 = 38.4 years.
And the present age of B = 2x = 2 * 12.8 = 25.6 years.
Requested by: Ahmed
Question 2:
The sum of the present ages of a father and his son is 48 years. Four years ago, the father’s age was five times the age of the son. Find their present ages.
Solution:
Let the present age of the son be x. Therefore, the present age of the father is 48 – x.
According to the given information, 48 – x – 4 = 5(x – 4).
Simplifying the equation, 48 – x – 4 = 5x – 20.
Combining like terms, 44 – x = 5x – 20.
Bringing like terms to one side, 6x = 64.
Dividing both sides by 6, we get x = 10.67.
Therefore, the present age of the son is approximately 10.67 years.
And the present age of the father is approximately 48 – 10.67 = 37.33 years.
Requested by: Ahmed
Question 3:
The average age of a family of 5 members is 24 years. If the youngest member is 8 years old, what is the average age of the family excluding the youngest member?
Solution:
The sum of the ages of the family members is 24 * 5 = 120 years.
Since the youngest member is 8 years old, the sum of the ages of the remaining 4 members is 120 – 8 = 112 years.
Therefore, the average age of the family excluding the youngest member is 112/4 = 28 years.
Requested by: Inaam
Question 4:
The present age of a father is four times the age of his son. The difference between their ages is 20 years. Find their present ages.
Solution:
Let the present age of the son be x. Therefore, the present age of the father is 4x.
According to the given information, 4x – x = 20.
Simplifying the equation, 3x = 20.
Dividing both sides by 3, we get x = 6.67.
Therefore, the present age of the son is approximately 6.67 years.
And the present age of the father is approximately 4 * 6.67 = 26.67 years.
Requested by: Faisal
Question 5:
The ratio of the present ages of A and B is 5:3. If the difference between their ages is 8 years, find their present ages.
Solution:
Let the present age of A be 5x and B be 3x.
According to the given information, 5x – 3x = 8.
Simplifying the equation, 2x = 8.
Dividing both sides by 2, we get x = 4.
Therefore, the present age of A = 5x = 5 * 4 = 20 years.
And the present age of B = 3x = 3 * 4 = 12 years.
Requested by: Faisal
Question 6:
The average age of a group of 8 friends is 32 years. If the age of one of the friends is 40 years, what is the average age of the remaining friends?
Solution:
The sum of the ages of the 8 friends is 32 * 8 = 256 years.
Since one of the friends is 40 years old, the sum of the ages of the remaining 7 friends is 256 – 40 = 216 years.
Therefore, the average age of the remaining friends is 216/7 ≈ 30.86 years.
Requested by: Zohaib
