"Age" problems are a common and important part of Logical Reasoning in various competitive exams. These problems test your ability to form equations based on age-related relationships and to solve them logically. Though they may seem simple, they often involve tricky language or multiple variables.
📘 Types of Age Problems
1. Present Age Problems
These are based on the current ages of individuals.
Example:
Ravi is 5 years older than Sita. If Sita is 20 years old, what is Ravi’s age?
👉 Solution: Ravi = 20 + 5 = 25 years
2. Past Age Problems
Involve ages from a certain number of years ago.
Example:
5 years ago, A was twice as old as B. Their current age difference is 10 years. Find their present ages.
👉 You’ll need to form and solve equations.
3. Future Age Problems
These involve ages after a certain time.
Example:
In 5 years, the age of A will be three times B's age. Find the current ages.
4. Age Comparison Problems
Compare ages between two or more individuals using ratios or differences.
Example:
The ratio of ages of A and B is 4:3. After 6 years, the ratio becomes 10:9. Find their present ages.
5. Cumulative or Family Age Problems
These involve ages of multiple people, like family members.
Example:
The sum of the ages of a father and his son is 45 years. Five years ago, the father was four times the age of the son. Find their current ages.
🔧 Tips & Techniques
-
Assume Present Age as a Variable
Example: Let the present age of A be x years. -
Translate Words into Equations
-
“5 years ago” → (x - 5)
-
“In 3 years” → (x + 3)
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“Twice the age” → 2x
-
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Use Ratios Carefully
If A : B = 3 : 4, then assume A = 3x and B = 4x. -
Form Equations & Solve Step-by-Step
✍️ Examples with Solutions
Example 1: Present Age
Question:
The present age of Rahul is twice the present age of his brother. After 5 years, the ratio of their ages will be 9:5. What is Rahul's present age?
Solution:
Let brother's present age = x
Then Rahul’s age = 2x
After 5 years:
Rahul = 2x + 5
Brother = x + 5
Now,
(2x + 5) / (x + 5) = 9 / 5
Cross-multiplying:
5(2x + 5) = 9(x + 5)
10x + 25 = 9x + 45
10x - 9x = 45 - 25
x = 20
Rahul’s age = 2x = 40 years
Example 2: Ratio and Future Age
Question:
The present age of A and B is in the ratio 5:4. After 8 years, their ages will be in the ratio 13:11. Find their present ages.
Solution:
Let present ages be:
A = 5x
B = 4x
After 8 years:
A = 5x + 8
B = 4x + 8
Now,
(5x + 8) / (4x + 8) = 13 / 11
Cross-multiplying:
11(5x + 8) = 13(4x + 8)
55x + 88 = 52x + 104
55x - 52x = 104 - 88
3x = 16
x = 16/3 ≈ 5.33
So,
A = 5x = 26.67 years
B = 4x = 21.33 years
(If required, leave the answer in fractions or round appropriately.)
✅ Practice Questions with Answers and Analysis
Q1. The sum of the ages of a father and his son is 60 years. 5 years ago, the father was four times as old as the son. What are their current ages?
Answer:
Let son’s age = x
Father’s age = 60 - x
Five years ago:
Father = 60 - x - 5 = 55 - x
Son = x - 5
Now,
55 - x = 4(x - 5)
55 - x = 4x - 20
55 + 20 = 4x + x
75 = 5x
x = 15
Son = 15, Father = 60 - 15 = 45 years
Analysis:
Translate the language to math correctly. Don’t forget to subtract years from both individuals when going into the past.
Q2. The ratio of the ages of A and B is 3:5. After 6 years, the sum of their ages will be 54. What are their current ages?
Answer:
Let A = 3x, B = 5x
After 6 years:
A = 3x + 6, B = 5x + 6
Sum = (3x + 6) + (5x + 6) = 8x + 12 = 54
8x = 42
x = 5.25
A = 3x = 15.75, B = 5x = 26.25
Analysis:
Even when the result isn’t a whole number, don't panic. Some reasoning problems will involve decimal or fractional ages.
Q3. A is 5 years older than B. After 3 years, A will be twice as old as B. Find their present ages.
Answer:
Let B’s present age = x
Then A = x + 5
After 3 years:
A = x + 5 + 3 = x + 8
B = x + 3
Now,
x + 8 = 2(x + 3)
x + 8 = 2x + 6
8 - 6 = 2x - x
x = 2
So B = 2, A = 7
Analysis:
This question tests how well you track years ahead. Be precise with the "after" condition.
