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Age Arithmetic Progression

Age Arithmetic Progression problems involve ages that form an arithmetic progression (AP). These problems test your understanding of AP concepts applied to age sequences over time.

10Worksheets
200+Practice Questions
AdvancedDifficulty
3-4 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Age Arithmetic Progression

Age Arithmetic Progression problems involve ages that form an arithmetic progression (AP). These problems test your understanding of AP concepts applied to age sequences over time.

Prerequisites

Arithmetic Progression basics nth term of AP Sum of AP terms Linear equations
Why This Matters: Age AP problems appear in 1-2 questions in advanced exams like CAT and banking mains. They test sequence and series concepts.

How to Solve Age Arithmetic Progression Problems

1

Step 1: Let the ages in AP be a-d, a, a+d (for 3 persons)

2

Step 2: For n persons, use a, a+d, a+2d, ..., a+(n-1)d

3

Step 3: Use given sum of ages to find relationship between a and d

4

Step 4: Use given ratios or other conditions to form second equation

5

Step 5: Solve for a (middle term) and d (common difference)

6

Step 6: Calculate individual ages

7

Step 7: Verify that ages are in AP and satisfy all conditions

Pro Strategy: For three terms in AP, use a-d, a, a+d. The middle term a equals the average. For even number of terms, use a-3d, a-d, a+d, a+3d pattern.

Example Problem

Example: Ages of three siblings are in arithmetic progression. The sum of their ages is 45 years. The oldest is 10 years older than the youngest. Find their ages. Solution: Step 1: Let ages be a-d, a, a+d Step 2: Sum = (a-d) + a + (a+d) = 3a = 45 → a = 15 Step 3: Oldest - Youngest = (a+d) - (a-d) = 2d = 10 → d = 5 Step 4: Ages: 15-5=10, 15, 15+5=20 years Answer: 10, 15, 20 years

Pro Tips & Tricks

  • For 3 terms: a-d, a, a+d → sum = 3a
  • For 4 terms: a-3d, a-d, a+d, a+3d → sum = 4a
  • The middle term(s) give the average directly
  • Age differences are multiples of the common difference d
  • Ages usually increase (d positive)
  • d must be such that youngest age > 0

Shortcut Methods to Solve Faster

Sum of 3 AP terms = 3 × middle term
Sum of 4 AP terms = 4 × average of middle two
Difference between oldest and youngest = (n-1)d

Common Mistakes to Avoid

Using wrong representation for AP (using a, a+d, a+2d for 3 terms is also valid but more complex)
Forgetting that ages must be positive
Not verifying that the common difference is constant
Assuming ages are in AP when not explicitly stated

Exam Importance

Age Arithmetic Progression is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
0-1 questions
BANKING PO
1-2 questions
RAILWAYS RRB
1-2 questions
CAT
1-2 questions
INSURANCE
0-1 questions

Ready to Master Age Arithmetic Progression?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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