Problems on Ages — The Complete Basics
Learn the one-variable method for age problems: handling past and future ages, the constant-difference rule, and ratio-based questions for SSC-CGL.
By the PadhoDost Team · 📖 6 min read · Updated 4 August 2026
Part of SSC CGL & Banking prep🧠 Two Runners on Parallel Tracks
Picture two people born a few years apart, walking side by side through life. The gap between their ages never changes — if A is 5 years older today, A stays 5 years older forever. That single truth, the constant difference, quietly solves a huge share of age problems.
The winning habit is to fix everything to the present. Let a person's present age be a variable like x. Then 'n years ago' means x - n and 'n years hence' means x + n. Translate each sentence of the problem into an equation using these, and solve. No memorised tricks needed — just careful translation.
The Golden Rules
| Time frame | Person A (now = a) | Person B (now = b) |
|---|---|---|
| n years ago | a - n | b - n |
| Present | a | b |
| n years hence | a + n | b + n |
📝 A ratio problem, step by step
The present ages of A and B are in the ratio 4 : 5. After 5 years, the ratio becomes 5 : 6. Find their present ages.
Let the present ages be 4x and 5x (this keeps the ratio 4 : 5 automatically).
After 5 years: A = 4x + 5, B = 5x + 5, and their ratio is 5 : 6.
So (4x + 5) / (5x + 5) = 5 / 6. Cross-multiply: 6(4x + 5) = 5(5x + 5).
24x + 30 = 25x + 25 -> 30 - 25 = 25x - 24x -> x = 5.
Present ages: A = 4x = 20 years, B = 5x = 25 years. Check: after 5 years, 25 : 30 = 5 : 6. Correct.
A reliable method for any age sum
- 1Assign a variable to the present age (use x, or 4x and 5x if a ratio is given).
- 2Express every other age as present age plus or minus the stated years.
- 3Turn each condition in the problem into one equation.
- 4Solve the equation(s) for the variable.
- 5Substitute back to get actual ages, then verify against the original statement.
Keep these handy
- ✓Always anchor to present age and build past/future from it.
- ✓The difference between two people's ages is constant for all time.
- ✓For ratio questions, write ages as 4x and 5x so the ratio holds by itself.
- ✓Add the years first, then form the new-ratio equation — order matters.
- ✓Always plug your answer back in to confirm it fits every condition.
⚡ Quick check
A father is 3 times as old as his son. After 12 years, the father will be twice as old as his son. What is the son's present age?
Ready to test yourself? 🎯
Lock it in with the practice test for this chapter.
Take the practice test →