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
3graded MCQs · easy to hard · full solution & trap analysis
The ratio of the present ages of Arun and Bhavna is 5:3. If Arun is 10 years older than Bhavna, what will be the ratio of their ages after 6 years?
Practice 2medium
The ratio of the present ages of Arun and Bhavna is 5:7. Four years ago, the ratio of their ages was 3:5. What will be Arun's age after 6 years?
Practice 3hard
The ratio of the present ages of Arun and Bhavna is 4:5. Five years ago, the ratio of their ages was 3:4. After how many years from now will the ratio of their ages be 6:7?
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