Problems on Ages
Problems on Ages are really linear-equation problems wearing a story. The whole chapter rests on one quiet fact: time moves everyone forward by the same amount. If a person is x years old today, then t years ago that person was (x − t) and t years from now will be (x + t). The same constant t shifts every age in the question, which keeps the differences between two people fixed forever — only the ratio between their ages changes as the years pass. CAT and the other exams (XAT, SNAP, NMAT, CMAT) rarely ask a bare "find the age" question; they bury the same skill inside ratio-and-proportion sets, averages, and data-arrangement puzzles, and they punish students who set up sloppy variables. This chapter teaches the clean method: name the present age once, shift it by the same t for the past or future, and combine a ratio with a known difference to pin down exact values. We cover present-and-past framing, age-ratio problems and the "ratio changes over time" trap, and future-age set-ups — each with worked CAT-style examples, the fastest set-up, and the errors that quietly cost marks.
Topics
⚡ CAT shortcuts & speed methods
The fastest ways to crack this chapter under time pressure — the techniques that separate a 95+ percentiler from the rest.
- Name the PRESENT age once; reach past with (x − t) and future with (x + t). Never invent a second variable for a shifted age.
- The age difference is permanent: (A − B) today equals (A − B) at any past or future time — anchor on it.
- Ratio m:n ⇒ write mk and nk; a known difference gives (n − m)k = diff, so k drops out in one line.
- Two-ratio problems (now and later): set (mk + t)/(nk + t) equal to the second ratio and solve for k.
- "In t years A is twice B" with gap d: then B + t = d, so B = d − t directly — skip the full system.
- Sum-of-ages clue: sum after t years = present sum + (number of people) × t. Useful with averages.
⚠️ Common mistakes & traps
CAT is designed so that careless errors here cost you marks. Internalise each trap before the exam.
- Assuming the age ratio stays constant over time — only the difference is fixed; the ratio drifts toward 1:1.
- Creating a fresh variable for a past or future age instead of shifting the present-age variable by ±t.
- Misreading "ago" vs "hence" and using the wrong sign on t.
- Applying the same t-shift to a ratio multiplier k by mistake (shift the ages mk and nk, not k itself).
- Forgetting that "was twice as old" links a past expression to a past expression — keep both clauses on the same timeline.
📈 CAT exam insight & PYQ analysis
🎴 Flashcards — instant recall
Tap a card to reveal the answer. Drill these until they are automatic.
📌 Quick revision
Chapter test
🏆 Vidaara CAT success checklist
You have truly mastered Problems on Ages when you can tick every box below.
- Recall every formula in this chapter without looking them up
- Solve each topic’s practice set with at least 80% accuracy
- Use the chapter shortcuts to cut your solving time in half
- Spot and avoid every common trap listed above
- Score 80%+ on the timed chapter test
📋 Chapter mastery scorecard
Track where you stand. Aim for the target before moving to the next chapter.
| Skill checkpoint | Target |
|---|---|
| Concept theory & formulas understood | 100% |
| Topic practice sets attempted (3 topics) | 3/3 |
| Best topic-test score | — → 80%+ |
| Chapter test score | — → 80%+ |
| Flashcards drilled to instant recall | 12 cards |
Formula Reference Sheet
Time-shift identities
| Present age | Let present age = x years |
|---|---|
| Age t years ago | x − t |
| Age t years hence | x + t |
| Difference is constant | (a + t) − (b + t) = a − b (never changes) |
| Sum after t years | (a + t) + (b + t) = a + b + 2t |
Ratio power-tools
| Ratio to actual values | If ages are in ratio m:n, take them as mk and nk |
|---|---|
| Fixed difference fixes k | nk − mk = (n − m)k = known difference |
| Ratio now vs later | m:n at present need not stay m:n after t years |
| Average of N people | Sum of ages = N × average age |
| A is k times B now | A = kB, then shift both by ±t for past/future |