To solve the problem, let's define the variables and set up the equations based on the information given:
- Let the present age of Jean be \(x\) years.
- According to the problem, John is twice as old as Jean. Therefore, John's present age is \(2x\) years.
- It is given that after 3 years, the sum of their ages will be 66 years. In 3 years, Jean's age will be \((x + 3)\) and John's age will be \((2x + 3)\).
- Set up the equation for the sum of their ages after 3 years: \((x + 3) + (2x + 3) = 66\)
- Simplify the equation:
- \(x + 3 + 2x + 3 = 66\)
- \(3x + 6 = 66\)
- Subtract 6 from both sides: \(3x = 60\)
- Divide by 3: \(x = 20\)
- So, Jean's present age is \(20\) years and John's present age is \(2 \times 20 = 40\) years.
Therefore, the present ages of Jean and John are 20 years and 40 years, respectively.
The correct answer is 20 and 40 years.
Let's verify this solution:
- Jean's age after 3 years: \(20 + 3 = 23\) years.
- John's age after 3 years: \(40 + 3 = 43\) years.
- Sum of their ages after 3 years: \(23 + 43 = 66\) years, which matches the given condition.
This confirms that our solution is correct. The answer is validated.
Similar Questions
- Narendra's mother is four times as old as Narendra. Four years ago, his mother was six times as old as Narendra was. What are their Present ages?
- A mother is now three times as old as her daughter. 5 years ago, she was four times as old as her daughter. What is the current age of the daughter?
- If 3 times a mother's present age is 24 years more than 9 times her daughter's present age, and 4 times the daughter's present age is 2 years less than the mother's present age, then what is the difference (in years) between the ages of the mother and the daughter?
- The ages of A and B are in the ratio of 5 : 3. After 5 years the ratio of their ages will be 10 : 7. What is the difference between present ages of A and B(in years)?
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- The sum of the reciprocals of the ages of two colleagues is nine times the difference of the reciprocals of their ages. If the ratio of the products of their ages to the sum of their ages is 100 : 9, Find their ages.
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- A father is 3 times as old as his son today. After 13 years the father will be twice as old as his son. The present age of the son is:
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Important Questions from Problems on Age
The age of Dr. Pandey is four times the age of his son. After 10 years, the age of Dr. Pandey will be twice the age of his son. The present age of Dr. Pandey's son is?
Three years ago, the average age of a family of six members was 19 years. Since then, a boy has been born, and the average age of the family is the same today as it was three years ago. What is the age of the boy?
Amita is 2 years older than her friend Amrita. Amita's father is twice as old as Amita, and Amrita is twice as old as her sister. The ages of Amita's father and Amrita's sister differ by 43 years. The sum of the ages (in years) of Amita and Amrita is:
- Narendra's mother is four times as old as Narendra. Four years ago, his mother was six times as old as Narendra was. What are their Present ages?
- A mother is now three times as old as her daughter. 5 years ago, she was four times as old as her daughter. What is the current age of the daughter?
