Problems on Age
“Problems on Ages” are a category of mathematical problems that involve determining the ages of individuals based on given conditions or relationships between their ages at different points in time. These problems often require setting up and solving algebraic equations.
Key Concepts for Problems with Age
- Present Age: The current age of a person.
- Future Age: The age of a person after a certain number of years.
- Past Age: A person’s age certain number of years ago.
- Age Difference: The difference in ages between two individuals, remains constant over time.
- Sum of Ages: The combined ages of two or more individuals.
- Age Ratios: The relationship between the ages of two individuals expressed as a ratio.
Problems with Age Formula
- If the current age is x, then n times the age is nx.
- If the current age is x, then age n years later/hence = x + n.
- If the current age is x, then age n years ago = x – n.
- The ages in a ratio a: b will be ax and bx.
- If the current age is x, then 1/n of the age is x/n.
Steps to Solve Age Problems:
- Define Variables: Assign variables to the unknown ages. For example, let x be the present age of a person.
- Set Up Equations: Based on the problem’s conditions, set up one or more equations.
- Solve Equations: Use algebraic methods to solve the equations for the variables.
- Verify Solutions: Plug the solution back into the original conditions to ensure they are satisfied.
Common Scenarios
1. Simple Age Calculation
Example: A person is 20 years older than their son. If the son’s age is x, then the person’s age is x+20.
2. Sum of Ages
Example: The sum of the ages of a father and his son is 50 years. If the son’s age is x, then the father’s age is 50−x.
3. Age Difference
Example: The age difference between two friends is 5 years. If one friend’s age is x, the other friend’s age is x+5 or x−5.
4. Ratio of Ages
Example: The ratio of the ages of two siblings is 3:2. If the younger sibling’s age is x, then the older sibling’s age is 3/2x.
5. Future and Past Ages
Example: A person will be twice as old as their current age in 10 years.
Present age = x
Age in 10 years = x+10
ATQ, x+10 = 2x
x = 10
Tricks to Solve Problems on Ages
- Define Clear Variables:
- Always define your variables clearly. Typically, use x for the present age of the person you know the least about.
- For example, let x be the present age of the younger person if dealing with two people.
- Translate Words into Equations:
- Carefully translate the verbal statements into mathematical equations.
- For example, if someone is twice as old as another, write it as x=2yx = 2yx=2y.
- Use Consistent Units of Time:
- Make sure all ages are represented in the same units (e.g., years).
- Be mindful of whether the problem refers to present age, age in the past, or age in the future.
- Set Up Equations for Different Periods:
- For problems involving different periods, set up separate equations for each period.
- For instance, if considering ages 5 years ago or 10 years in the future, clearly write equations for those ages.
- Keep Track of Relationships:
- Remember that the age difference between two people remains constant over time.
- If the age difference between two people is given, it simplifies setting up the equations.
- Check Your Equations:
- After setting up the equations, re-read the problem to ensure all conditions are accounted for correctly.
- Solve Systematically:
- Solve the equations step-by-step. If dealing with more than one variable, use substitution or elimination methods.
- Start by simplifying one equation, then substitute it into the other.
- Verify Solutions:
- After finding the solution, plug the values back into the original conditions to ensure they fit all parts of the problem.
Weightage of Problems on Age Questions
Exam-wise Weightage
- IBPS PO & Clerk:
- Typically, 1-2 questions on age.
- The Quantitative section usually has 35 questions, so age problems may constitute around 3-6% of this section.
- SBI PO & Clerk:
- Similar to IBPS, expect 1-2 questions on age.
- The Quantitative section has around 35 questions, meaning age problems represent about 3-6% of the section.
- RBI Grade B:
- Quantitative aptitude is a crucial part of the preliminary exam.
- You might encounter 1-2 questions on age, contributing to the overall 35-40 questions.
- Other Banking Exams:
- Exams like NABARD, LIC AAO, and others also feature similar patterns, with 1-2 questions on ages being a common trend.
Problems on Age Solved Questions
Previous Year Questions Of Problem on Ages
Q1. The present age of a man is four times the age of his son. Four years ago, the man’s age was five times the age of his son. Find their present ages.
Q2. The sum of the ages of a mother and her daughter is 50 years. Ten years ago, the mother was three times as old as her daughter. Find their present ages.
Q3. The present age of a mother is three times the present age of her daughter. After 5 years, the age of the mother will be twice the age of the daughter. What is the present age of the mother?
Q4. The present age of a father is 24 years more than the present age of his son. After 6 years, the father’s age will be two times the age of his son. Find their present ages.
Q5. A person is 4 times as old as his son. 8 years ago, the person was 10 times as old as his son. What are their present ages?
Q6. The sum of the present ages of a father and his son is 60 years. 6 years ago, the father’s age was 5 times the age of his son. Find their present ages.
Q7. The present age of a woman is twice the age of her daughter. After 10 years, the woman will be 1.5 times the age of her daughter. Find their present ages.
Q8. The present age of Rahul is 5 years more than three times the present age of his son. If the sum of their ages is 35 years, what is the present age of Rahul’s son?
Q9. The ratio of the ages of a father and his son is 7:3. After 6 years, the ratio of their ages will be 5:3. Find their present ages.
Q10. The present age of a mother is twice the age of her daughter. Ten years ago, the mother was three times as old as her daughter. Find their present ages.
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Problem on Ages FAQs
Ans. Direct age relationships: Involves comparing the ages of two or more individuals directly, such as "A is twice as old as B." Sum of ages: Deals with the total of the ages of two or more individuals. Difference in ages: Focuses on the age gap between individuals. Future and past ages: Involves calculating ages after a certain number of years or before a certain number of years. Age ratios: Compare the ages using ratios, such as "The ratio of A's age to B's age is 3:2."
Ans. Identify variables: Assign variables to the unknown ages. Translate words into equations: Convert the given information into algebraic equations. Solve the equations: Use algebraic methods like substitution or elimination to find the values of the variables. Verify the solution: Check that the solution satisfies all the given conditions.
Ans. Incorrect equation setup: Misinterpreting the relationships can lead to incorrect equations. Ignoring constant differences: The age difference between two people remains constant over time. Not verifying solutions: Always check your solution against the problem statement to ensure accuracy.
Ans. Practice regularly: The more problems you solve, the quicker you’ll recognize patterns and setups. Learn shortcuts: Familiarize yourself with common tricks and shortcuts for age problems. Time yourself: Practice under timed conditions to improve speed.
Ans, Yes, age problems are a staple in competitive exams like banking exams (IBPS, SBI, RBI), SSC, and other aptitude tests. They test basic algebraic skills and logical thinking.
Ans. Age-related problems generally range from easy to moderate difficulty. They often require basic algebraic manipulation and logical reasoning.
Ans. Future age: If someone’s age will be a certain value in n years, add n to their current age. Example: If A is x years old now, in 5 years A will be x+5. Past age: If someone’s age was a certain value n years ago, subtract n from their current age. Example: If A is x years old now, 5 years ago A was x−5.
Ans. The age difference between two people remains constant over time. Use this constant difference to set up your equations and simplify the problem-solving process.