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.
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Formula Block
Memorise — 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
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Exam Patterns
What 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.
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Shortcuts
Use 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.
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Worked Example
Solve 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 ✓
Common Mistake: 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.
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