CDS Mathematics · Linear Equations

Age Problems

Write every age as a present age plus or minus the years that have passed; each 'was' or 'will be' sentence is then one linear equation.

All Linear Equations notes CDS Mathematics strategy

Why this matters

Twelve PYQs, two of them HARD. Everyone ages at the same rate: n years ago each person was n younger, so a family of k people was kn years younger in total. Keep all ages in the present and the equations stay simple.

Concept 1 of 1: Past, present and future ages

Let the present ages be the unknowns. 'Five years ago' subtracts

5

from each; 'in four years' adds

4

. The difference between two people's ages never changes.

Definition

$n$ years ago: each age minus $n$ ; a group of $k$ people is $kn$ years younger in total.
The difference between two ages is the same at every time.
'Was three times as old' becomes $R - 5 = 3(S - 5)$ , not $R = 3S - 5$ .
The year the youngest was born, the others were younger by the youngest's present age.

n years ago

R - n = k(S - n)

Worked example

Four years ago

A

was four times as old as

B

. In six years

A

will be twice as old as

B

. Find

A

's present age.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2017 · CDS (II) 2017 — Elementary Mathematics · Q29Easy

Example 1 · Linear Equations · Age Problems

Five years ago, Ram was three times as old as Shyam. Four years from now, Ram will be only twice as old as Shyam. What is the present age of Ram ?

Subtract from both ages

'Five years ago Ram was three times as old as Shyam' is

R - 5 = 3(S - 5)

. Subtracting only from Ram's side gives the wrong equation.

Drill 11 more on past, present and future ages

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Past, present and future ages
n years ago
$R - n = k(S - n)$

Watch out for (1)

Subtract from both ages
→ Past, present and future ages

Test yourself on Linear Equations

15 past CDS questions from this chapter, timed at 18 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

Take the Linear Equations chapter test Drill all 12 questions