Overview: Ages | Quantitative Techniques for CLAT PDF Download

Understanding Age Problems

Age problems involve determining the present age of individuals, considering their past ages and future ages. These problems usually revolve around relationships between family members, friends or any group. The key is to translate the given information into equations and solve for the unknown variables.

Solving Age Problems: Concepts and Examples

Example 1: Present Ages
(i) The sum of Aarav’s age and Rahul’s age is 45. If Aarav is 5 years older than Rahul, what are their present ages?
Sol: Let A be Aarav’s age and R be Rahul’s age.
From the information given, we have the equations:

• A + R = 45 (Sum of ages)
• A = R + 5 (Aarav is 5 years older than Rahul)

Substitute the second equation into the first equation:
(R + 5) + R = 45
2R + 5 = 45
2R = 40
R = 20 (Rahul’s age)
Substitute Rahul’s age into the second equation to find Aarav’s age:
A = 20 + 5
A = 25 (Aarav’s age)

Example 2: Age Differences
(i) Alex is 15 years older than Bella. In 5 years, Alex’s age will be twice Bella’s age. What are their present ages?
Sol:
Let A be Alex’s age and B be Bella’s age.
From the information given, we have the equations:

• A = B + 15 (Alex is 15 years older)
• A + 5 = 2(B + 5) (In 5 years, Alex will be twice Bella’s age)

Substitute the first equation into the second equation:
(B + 15) + 5 = 2(B + 5)
B + 20 = 2B + 10
B = 10 (Bella’s age)
Substitute Bella’s age into the first equation to find Alex’s age:
A = 10 + 15
A = 25 (Alex’s age)

Strategies for Tackling Age Problems

Tackling age-related problems requires logical thinking and translating the given information into equations. Here are strategies to help you approach these problems effectively:

• Define Variables: Define variables for unknown ages and express the relationships using these variables.
• Form Equations: Translate the given information into equations based on the relationships between ages.
• Solve Simultaneous Equations: Solve the equations simultaneously to find the values of the unknown ages.
• Check Reasonability: After solving, check if the ages are reasonable and satisfy the conditions given in the problem.
• Practice Regularly: Practice a variety of age-related problems to improve your problem-solving skills and accuracy.

Conclusion

Age problems might seem complex at first, but with a solid understanding of the fundamental concepts and regular practice, you can handle them confidently. Remember to define variables, form equations, solve simultaneous equations, check solutions for reasonability and practice regularly. As you prepare for the CLAT, mastering age-related problems will not only enhance your quantitative aptitude skills but also boost your overall confidence in approaching competitive exams.