Module 1 · Arithmetic
Chapter 15: Problems on Ages
Arithmetic
3 topics
What this chapter covers
The 3 topics below make up Problems on Ages on the CAT. Click any topic to open its notes, examples and practice test.
Study material & tests
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📝 Chapter test
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Formula Reference Sheet
This chapter
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 |
CAT reference
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