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
23graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 23
The ratio of the ages of Arun and Bhavna is 5:3. If Arun is 20 years old, what is Bhavna's age?
Practice 2easy
The sum of the ages of Arjun and Bheem is 48 years. The ratio of their ages is 5:7. What is Bheem's age?
Practice 3easy
The ratio of ages of Ravi and Sita is 7:5. The sum of their ages is 48 years. What is Ravi's age?
Practice 4easy
The ratio of ages of Mira and Nisha is 7:5. Four years hence, their ages will be in the ratio 11:9. What is Mira's current age?
Practice 5easy
The ratio of the present ages of Aman and Bina is 3:2. After 6 years, their ages will be in the ratio 5:4. What is Aman's present age?
Practice 6easy
The ratio of the present ages of Esha and Faisal is 6:5. After 6 years, the ratio of their ages will be 7:6. What is Esha's present age?
Practice 7easy
Chitra's age is 3 times Deepak's age. If the sum of their ages is 40 years, what is Deepak's age?
Practice 8easy
Five years ago, the ratio of Priya's age to Qasim's age was 4:5. If Qasim is currently 30 years old, what is Priya's current age?
Practice 9medium
Gita's age is 3/4 of Hari's age. After 6 years, Gita's age will be 5/6 of Hari's age. What is the difference between their present ages?
Practice 10medium
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 11medium
The present ages of Meera and Nisha are in the ratio 7:5. Six years hence, their ages will be in the ratio 5:4. What was the ratio of their ages 4 years ago?
Practice 12medium
The ratio of the present ages of Arun and Bhavna is 4:5. After 8 years, the ratio of their ages will be 6:7. What is Arun's present age?
Practice 13medium
Five years ago, the ratio of Chitra's age to Deepak's age was 3:4. Five years hence, the ratio will be 4:5. What will be Chitra's age after 10 years?
Practice 14hard
The ratio of Meera's age to Neha's age is 5:7. If Meera were 4 years older and Neha were 4 years younger, the ratio would be 1:1. What is the difference between their present ages?
Practice 15hard
Sanjay's age is 40% more than Tanya's age. Five years ago, Sanjay's age was 50% more than Tanya's age. What is Sanjay's present age?
Practice 16hard
The ratio of the present ages of Usha and Vimla is 6:5. After 6 years, the ratio will be 7:6. If Wina's present age is 2 years less than the average of Usha and Vimla's present ages, what is Wina's present age?
Practice 17hard
Aman's age is 3/5 of Bhumi's age. If Aman were 5 years older and Bhumi were 5 years younger, Aman's age would be 4/5 of Bhumi's age. What is the sum of their present ages?
Practice 18hard
The ratio of ages of A and B is 7:5. Four years ago, the ratio of their ages was 3:2. After how many years will the ratio of their ages be 9:7?
Practice 19hard
The ratio of ages of A, B, and C is 4:7:9. Six years ago, the sum of their ages was 62. After how many years will the ratio of ages of A and C be 3:5?
Practice 20hard
The ratio of ages of Meera and Neha five years ago was 5:4. The ratio of their ages five years hence will be 6:5. What is the ratio of their current ages?
3 more practice questions in the Study Panel
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