Core ConceptRead this first — the foundation of the topic
Core Concept
Age problems involve finding current ages or ages at specific times when given ratios between different people's ages. The key insight is that while individual ages change over time, age differences remain constant
Key Rules
First, age difference between two people never changes. If A is 5 years older than B today, A will always be 5 years older. Second, when we add or subtract the same number of years to different ages, their ratio changes. Third, present age problems often give ratios at two different time points.
Formula BlockMemorise — at least one formula appears in every paper
• If ratio of ages is a:b, then ages are ax and bx where x is common factor
• After n years: (current age + n)
• Before n years: (current age - n)
• Age difference = |ax - bx| = |a - b|x
Exam PatternsWhat examiners ask — read before attempting PYQs
SSC CGL typically asks three types - current age ratios with future/past conditions, age ratios at two different time points, and problems involving sum of ages with ratios. Questions often involve 2-3 people with time shifts of 2-10 years.
ShortcutsUse these to save 30–60 seconds per question
For two-time-point problems, use the 'difference method'. If ratio changes from a:b to c:d after n years, then (cx-ax) = (dx-bx) where x is the time difference. This eliminates one variable immediately.
Worked ExampleSolve this step-by-step before moving on
1
Step 1
Let current ages be 3x and 4x
2
Step 2
After 6 years, ages become (3x+6) and (4x+6)
3
Step 3
New ratio = (3x+6):(4x+6) = 4:5
4
Step 4
Cross multiply: 5(3x+6) = 4(4x+6)
5
Step 5
15x + 30 = 16x + 24
6
Step 6
30 - 24 = 16x - 15x
7
Step 7
6 = x
8
Step 8
Current ages are 3×6 = 18 years and 4×6 = 24 years
Verification: After 6 years, ages are 24 and 30, ratio = 24:30 = 4:5 ✓
Exam TrapsCommon mistakes students make — avoid these
Students often forget to add/subtract years from both ages equally. Another error is setting up wrong equations when dealing with 'before' scenarios - remember to subtract years, not add them.
Key Points to Remember
Age difference between two people remains constant throughout their lives
Current ages in ratio a:b can be written as ax and bx
After n years formula: current age + n, Before n years: current age - n
When same number is added to numerator and denominator, ratio changes
Cross multiplication method works best for solving age ratio equations
Sum of ages increases by (number of people × years passed)
Two time-point problems require setting up two separate ratio equations
Always verify your answer by checking if it satisfies given conditions
Exam-Specific Tips
Age problems appear in 1-2 questions per SSC CGL Tier-1 paper consistently
Most common time shifts asked are 2, 3, 4, 5, 6, 8, and 10 years
Three-person age problems have appeared in 15% of recent SSC papers
Father-son age problems typically use ratios like 5:2, 7:3, or 9:4
Age sum problems often involve total ages of 60, 80, 100, or 120 years
Present age is usually a multiple of the ratio terms in 80% of questions
Negative age solutions indicate error in problem setup or calculation
Practice MCQs
Ages Problems — Practice Questions
13graded MCQs · easy to hard · full solution & trap analysis
Ravi's age is 3/4 of Sanjay's age. If Sanjay is 32 years old, what is Ravi's age?
Practice 2easy
Five years ago, the ratio of Priya's age to Deepak's age was 4:5. If Deepak is currently 35 years old, what is Priya's current age?
Practice 3easy
The ratio of the present ages of Arun and Bhavna is 5:3. If Arun is 20 years older than Bhavna, what is Bhavna's present age?
Practice 4easy
The ratio of ages of Mohan and Sohan is 7:5. After 6 years, the ratio will be 4:3. What is Mohan's current age?
Practice 5easy
The ratio of ages of three friends Aman, Bhavesh, and Chitra is 2:3:4. If the sum of their ages is 54 years, what is Chitra's age?
Practice 6medium
The ratio of ages of Rohan and Sohan is currently 4:5. If Rohan was 8 years old when Sohan was 10 years old, what will be the ratio of their ages after 12 years?
Practice 7medium
Meera's age is 2/3 of Neha's age. After 10 years, Meera's age will be 4/5 of Neha's age. What is Neha's present age?
Practice 8medium
Yash is currently 3 times as old as Zara. In 8 years, Yash will be twice as old as Zara. What is the difference between their present ages?
Practice 9hard
The ratio of Meera's age to Neha's age is 5:4. After 8 years, the ratio will be 7:6. If Priya's present age is 2 years more than Meera's present age, what is Priya's present age?
Practice 10hard
The ratio of Arjun's age to Bhavna's age 4 years ago was 3:2. The ratio of their ages 4 years hence will be 5:4. In how many years from now will Arjun's age be 1.25 times Bhavna's age?
Practice 11hard
Divya's age is 40% more than Esha's age. Five years ago, Divya's age was 50% more than Esha's age. What is the ratio of Divya's present age to Esha's present age?
Practice 12hard
The ratio of Vikram's age to Wazir's age is 7:5. If Vikram is 8 years older than Wazir, and Xander's age is the average of their ages, what is the ratio of Vikram's age to Xander's age?
Practice 13hard
The ratio of ages of Arun and Bhavna 5 years ago was 4:5. The ratio of their ages 5 years hence will be 5:6. What is the sum of their present ages?
60-Second Revision — Ages Problems
Formula: Ages in ratio a:b = ax and bx where x is common multiplier
Remember: Age difference = constant, so |older age - younger age| never changes
Trick: For ratio change problems, cross multiply (3x+n):(4x+n) = p:q
Trap: Don't forget to add/subtract years from both ages in future/past scenarios
Check: Always verify final answer satisfies both given conditions
Pattern: If ages are in ratio 3:4 now and 4:5 later, set up two equations