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.
Vikram's age is twice the age of Ananya. If the sum of their ages is 45 years, what is Ananya's age?
Practice 2easy
The ratio of the ages of Arun and Bhavna is 5:3. If Arun is 20 years old, what is Bhavna's age?
Practice 3easy
Five years ago, the ratio of Priya's age to Deepak's age was 2:3. If Deepak is currently 30 years old, what is Priya's current age?
Practice 4easy
The ratio of ages of Meera and Neha is 3:4. If the sum of their ages is 56 years, what is Meera's age?
Practice 5easy
The ratio of the present ages of Arjun and Bheem is 7:5. If Arjun is 14 years older than Bheem, what is Bheem's current age?
Practice 6medium
The ratio of ages of Mohan and Sohan is 3:4. If Mohan is 9 years younger than Sohan, what will be the ratio of their ages after 7 years?
Practice 7medium
Divya is twice as old as Esha. Five years ago, Divya was three times as old as Esha. What is Esha's present age?
Practice 8medium
The ratio of ages of Aman and Bimal is 7:5. If the sum of their ages is 48 years, what will be Aman's age after 4 years?
Practice 9medium
Chitra's age is 5/4 times Diya's age. After 8 years, Chitra's age will be 6/5 times Diya's age. What is Diya's present age?
Practice 10hard
Three years ago, the ratio of ages of Priya and Qureshi was 4:5. Three years hence, the ratio will be 5:6. What is the sum of their present ages?
Practice 11hard
The ratio of the present ages of Arun and Bhavna is 5:7. Four years ago, the ratio of their ages was 3:5. After how many years will the ratio of their ages be 7:9?
Practice 12hard
Divya is currently twice as old as Esha. In 8 years, Divya's age will be 1.5 times Esha's age. What is the difference between their present ages?
Practice 13hard
The ratio of ages of Faisal and Gita is 5:6. If Faisal's age 4 years hence will be equal to Gita's age 2 years ago, what will be the ratio of their ages after 10 years?
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