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Quantitative Aptitude›Ch 1: Arithmetic Foundations›Problems on Ages
Master age ratio equations and time-gap shortcuts for SSC and Defence exams
The difference between ages of two persons always remains constant across time. Use ratio multipliers and time-gap equations to solve present, past and future ages instantly.
Memory Hooks
| Time Frame | Expression | Example (Age x) |
|---|---|---|
| Past (n years ago) | x - n | 25 - 5 = 20 |
| Present age | x | 25 years |
| Future (n years hence) | x + n | 25 + 5 = 30 |
Present Ratio
(Base multiplier setup)
Base multiplier setup
Let present ages be 3x and 4x.
Time Addition
(Add years to both)
Add years to both
After 5 years: (3x+5) and (4x+5).
New Ratio
(Equate to new ratio)
Equate to new ratio
Ratio becomes 4:5.
Solve x
(Find multiplier value)
Find multiplier value
Solve equation to get x = 5.
Adding years only to the younger personAdd years to all individuals in ratio
Time moves equally for everyone; add the gap to all persons.
Confusing past and future directionsSubtract for past, add for future
Always measure years relative to the present baseline.
Assuming age ratio stays constantAge ratio changes, age difference is constant
Ratios change with years, but absolute age gap remains fixed.
Q1.The ratio of present ages of A and B is 4:5. After 5 years, their ratio becomes 5:6. What is B's present age?
Q2.Father's age is 3 times the age of his son. After 10 years, he will be 2 times as old as his son. Find son's present age.