At present the average of the ages of a father and a son is 25 years. After seven years, the son will be 17 years old. What will be the age of father after 10 years?
50 years
Solving the Age Problem: Father and Son Ages
This question involves calculating the ages of a father and his son based on given information about their average age and the son's future age. We need to work step-by-step to find the current ages first and then calculate the father's age after 10 years.
Step 1: Find the Son's Current Age
We are given that the son will be 17 years old after seven years. To find the son's current age, we subtract 7 years from his age in the future.
Son's age after 7 years = 17 years
Son's current age = Son's age after 7 years \(\minus\) 7 years
Son's current age = \(17 \minus 7 = 10\) years
Step 2: Find the Sum of Current Ages
The average age of the father and son is given as 25 years. The average is calculated by dividing the sum of ages by the number of people. In this case, there are two people (father and son).
Average age = \(\frac{\text{Sum of ages}}{\text{Number of people}}\)
Sum of ages = Average age \(\times\) Number of people
Sum of current ages = \(25 \times 2 = 50\) years
This sum represents the combined current age of the father and the son.
Step 3: Find the Father's Current Age
We know the sum of their current ages (50 years) and the son's current age (10 years). We can find the father's current age by subtracting the son's current age from the sum of their current ages.
Sum of current ages = Father's current age \(\plus\) Son's current age
\(50 = \text{Father's current age} \plus 10\)
Father's current age = \(50 \minus 10 = 40\) years
Step 4: Find the Father's Age After 10 Years
The question asks for the father's age after 10 years from now. We already calculated the father's current age as 40 years.
Father's age after 10 years = Father's current age \(\plus\) 10 years
Father's age after 10 years = \(40 \plus 10 = 50\) years
Summary of Age Calculations
| Item | Calculation | Result |
|---|---|---|
| Son's Current Age | 17 years (in 7 years) \(\minus\) 7 years | 10 years |
| Sum of Current Ages | 25 years (average) \(\times\) 2 people | 50 years |
| Father's Current Age | Sum of Current Ages \(\minus\) Son's Current Age | \(50 \minus 10 = 40\) years |
| Father's Age After 10 Years | Father's Current Age \(\plus\) 10 years | \(40 \plus 10 = 50\) years |
The father's age after 10 years will be 50 years.
Revision Table: Key Concepts in Age Problems
| Concept | Explanation | Formula/Idea |
|---|---|---|
| Current Age | An individual's age at the present time. | This is the base age for calculations. |
| Future Age | Age after a certain number of years. | Current Age \(\plus\) Number of Years |
| Past Age | Age a certain number of years ago. | Current Age \(\minus\) Number of Years |
| Average Age | The mean age of a group of people. | \(\frac{\text{Sum of Ages}}{\text{Number of People}}\) |
| Sum of Ages | Total of the ages of all individuals in a group. | Average Age \(\times\) Number of People |
Additional Information: Tackling Age-Based Questions
Age-based problems are common in quantitative aptitude tests. They usually involve finding present or future/past ages based on relations given in the problem statement. Here are some tips:
- Always identify the reference point in time (present, past, or future).
- Assign variables (like x, y) if dealing with multiple unknown ages simultaneously, though simple problems might not require it.
- Formulate equations based on the relationships given (e.g., "father is twice as old as son," "age difference is 25 years," "average age is X").
- Solve the equations to find the unknown ages at the reference point, usually the present.
- Finally, calculate the required age (future or past) based on the age found in the previous step.
- Pay close attention to phrases like "after X years," "X years ago," "twice as old," "ratio of ages," and "average age."
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