Ages

The gap between two people's ages never changes. Anchor on the gap and every ratio question becomes counting units.

Start with this

Everyone gets older at the same speed. So the DIFFERENCE between two people's ages never changes.

Age questions are ratio and linear equations dressed up. Use the fact that the age gap is fixed, or just try the options.

The fixed gap, and the bar model

Worked example

The ratio of a father's age to his son's is 5 : 2. The father is 30 years older. Their ages?

1. The gap is 5 - 2 = 3 parts.
   Why: Bar model: 3 boxes.
2. 3 parts = 30, so 1 part = 10.
3. Father 50, son 20.

Answer: 50

Worked example

Four years ago, A was 3 times as old as B. In 4 years A will be twice as old as B. A's present age?

1. Let B four years ago = x, A = 3x. Now: A = 3x + 4, B = x + 4.
   Why: Start from the time the question describes first.
2. In 4 years: 3x + 8 = 2(x + 8).
3. x = 8.
4. A now = 28.

Answer: 28

Try the options

Age questions always have whole-number answers, and the options test directly: put the option in, check every sentence.

Worked example

The sum of the ages of a mother and daughter is 50. Five years ago the mother was 7 times as old as the daughter. Mother's age? (a) 35 (b) 40 (c) 42 (d) 45

1. Try 40: daughter 10. Five years ago: 35 and 5. 35 = 7 × 5. Fits.
   Why: Check both sentences.
2. 40.

Answer: 40

Shortcut: Ratio-units trick (no equations)

Use it when: 'Ratio now 4:5, 5 years ago 7:9'.

1. Differences: 5 - 4 = 1 unit, 9 - 7 = 2 units. Make them equal: now 8:10.
2. Now 8:10, then 7:9. Each person dropped 1 unit = 5 years.
3. So 1 unit = 5, ages 40 and 50.

Ratio-units trick (no equations): try it

A:B = 4:5 now, 7:9 five years ago. B's age?

1. Scale to 8:10 vs 7:9.
2. 1 unit = 5 years.
3. B = 10 × 5.

Answer: 50

Shortcut: Times-older problems

Use it when: 'Father is 3 times son now; in 15 years, twice'.

1. Now: 3:1, gap 2 units. Later 2:1, gap 1 unit → scale to 4:2.
2. Now 3:1, later 4:2: son went 1 → 2 units = 15 years.
3. Son 15, father 45.

Times-older problems: try it

Father's age?

1. 45.

Answer: 45

Your turn medium

Ten years ago A was half B's age. Their present ages are 3:4. Sum of present ages?

1. Now 3:4 (gap 1 unit). Then 1:2 (gap 1 unit) - gaps already match.
2. Each dropped 2 units (3 → 1, 4 → 2) = 10 years, so 1 unit = 5.
3. Ages 15 and 20, sum 35.

Answer: 35

Your turn medium

A is 4 years more than twice B's age; the product of their ages is 240. A's age?

1. b(2b + 4) = 240 → b = 10.

Answer: 24

Your turn medium

A couple's average age at marriage was 23. Five years later, with one child, the family's average age is 20. Child's age?

1. At marriage total 46; 5 years later 56.
2. Family of 3 total 60 → child 4.

Answer: 4

Your turn hard

A father's age is twice the sum of his two children's ages. In 20 years his age will equal the sum of theirs. Father's age now?

1. F = 2S. F + 20 = S + 40.
2. 2S + 20 = S + 40 → S = 20.

Answer: 40

Recap

• use the fixed age gap
• turn ratio statements into parts
• check options against every sentence

Now practise

11 questions with full solutions.

Open practice Back to the lesson