Age Difference Problem Explained
This problem involves finding the current ages of two people based on their age difference and a relationship between their ages in the past.
Setting Up the Equations
Let the present age of the older person be $x$ years and the present age of the younger person be $y$ years.
From the problem statement:
- The ages differ by 15 years: $x - y = 15$. (Equation 1)
- 5 years ago, the older person's age was $x - 5$ and the younger person's age was $y - 5$.
- The older person's age 5 years ago was twice the younger one's age: $x - 5 = 2(y - 5)$. (Equation 2)
Solving for Present Ages
We can solve these two equations simultaneously.
- Express $x$ in terms of $y$: From Equation 1, $x = y + 15$.
- Substitute into Equation 2: Replace $x$ in Equation 2 with $(y + 15)$. $(y + 15) - 5 = 2(y - 5)$
- Simplify and solve for $y$: $y + 10 = 2y - 10$ $10 + 10 = 2y - y$ $20 = y$ So, the younger person's present age is 20 years.
- Calculate $x$: Substitute $y = 20$ back into Equation 1 (or the expression for $x$). $x = y + 15 = 20 + 15 = 35$ So, the older person's present age is 35 years.
Conclusion
The present ages of the two persons are 35 years and 20 years.
Verification:
- Age difference: $35 - 20 = 15$ years. (Correct)
- 5 years ago: Older was $35 - 5 = 30$, Younger was $20 - 5 = 15$.
- $30 = 2 \times 15$. (Correct)
The calculated ages match the conditions given in the problem.
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?
- John is twice as old as Jean. After 3 years, the sum of their ages will be 66 years. What are the present ages of Jean and John, respectively?
- 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)?
- Age of A is 3 times more than that of B and half as that of C. If the sum of their ages is 120 years, what is the age (in years) of A?
- 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.
- The ratio of the present ages of Alok and Anil is 3 : 4. If Alok's age 20 years from now will be 62 years, then what is Anil's present age?
- 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:
- A is 6 years older than B. 10 years ago, B's age was three quarters of A's age. Find the present age (in years) of A.
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?
