11+ · Topic guide

Age and Difference Problems

Age and difference problems are word problems that compare two people's ages, or two quantities, at different points in time. The key fact examiners rely on is that the difference between two people's ages never changes, no matter how many years pass, even though the ratio between their ages does change; problems that give a sum and a difference can also be solved using the rule that the larger value equals half the sum plus half the difference.

Year 5-6 (11+)Maths and Numerical ReasoningGL AssessmentCEM

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Four Operations (Worded)Early Algebra

Method

Identify the ages or quantities being compared, and note carefully whether the question is set now, in the past, or in the future.
If it helps, represent an unknown age with a letter, writing the other person's age in terms of the same letter using the given relationship.
Remember that the difference between two people's ages stays exactly the same at every point in time, even though their ratio changes as they get older.
For 'sum and difference' problems, use larger = (sum + difference) / 2 and smaller = (sum - difference) / 2.
For ratio-based age problems, such as 'in 6 years the ratio will be...', write both ages in terms of the same letter using the current ratio, then form an equation from the future condition.
Check your final answer makes sense in context: ages should be positive, and the person described as older should still be older at every time mentioned in the question.

Worked example

Sam is 8 years older than his sister Priya. In 3 years, the sum of their ages will be 42. How old is Priya now?

Let Priya's current age be p. Since Sam is 8 years older, his current age is p + 8.
In 3 years, Priya will be p + 3 and Sam will be p + 8 + 3 = p + 11.
Their ages in 3 years sum to 42: (p + 3) + (p + 11) = 42.
Simplify: 2p + 14 = 42, so 2p = 28, giving p = 14.
Priya is 14 now (and Sam is 22). Check: in 3 years they will be 17 and 25, which sum to 42 and still differ by 8.

Practice questions

Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.

Q1Tom is 5 years older than Ella. Ella is 9. How old is Tom?Show answer

Answer: 14 (9 + 5)

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Q2The sum of two people's ages is 30 and their difference is 4. Find the two ages.Show answer

Answer: 17 and 13 (larger = (30+4)/2 = 17, smaller = (30-4)/2 = 13)

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Q3Maya is twice as old as her brother Leo. Maya is 16. How old is Leo?Show answer

Answer: 8 (16 / 2)

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Q4Five years ago, Ben was 9. How old is he now?Show answer

Answer: 14 (9 + 5)

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Q5The difference between two people's ages is 6 years. In 10 years' time, what will the difference between their ages be?Show answer

Answer: Still 6 years, since the age gap between two people never changes as time passes.

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Q6A mother is 24 years older than her daughter. The daughter is currently 11. How old will the mother be when the daughter is 20?Show answer

Answer: 44 (the age gap stays 24, so 20 + 24 = 44)

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Q7Two cousins' ages add up to 25, and one is 3 years older than the other. Find the older cousin's age.Show answer

Answer: 14 (larger = (25+3)/2 = 14, smaller = (25-3)/2 = 11)

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Q8A father is 30 years older than his son. If the son is 7, how old will the father be in 5 years' time?Show answer

Answer: 42 (father is now 37, and 37 + 5 = 42)

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Exam-style questions

Written in the style of a 11+ exam paper, with a full mark scheme.

Q1[4 marks]

Jack is 4 years older than his sister Freya. Six years ago, the sum of their ages was 22. How old is Jack now?

Show mark scheme

Tick each line you got. Your score builds from the marks on the scheme.

let Freya's current age be f, so Jack's current age is f + 4.1 mark
six years ago their ages were (f - 6) and (f + 4 - 6) = (f - 2); form the equation (f - 6) + (f - 2) = 22.1 mark
simplify to 2f - 8 = 22, so 2f = 30 and f = 15.1 mark
correct final answer, Jack is 19 now (Freya is 15). Check: six years ago they were 9 and 13, summing to 22 with a difference of 4.1 mark

Nothing ticked yet - 4 available

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Q2[5 marks]

Currently, the ratio of Mia's age to her uncle's age is 1 : 5. In 8 years, the ratio will be 1 : 3. How old is Mia now?

Show mark scheme

Tick each line you got. Your score builds from the marks on the scheme.

let Mia's current age be m; since the ratio is 1 : 5, her uncle's current age is 5m.1 mark
in 8 years their ages are (m + 8) and (5m + 8), in the ratio 1 : 3, giving 3(m + 8) = 5m + 8.1 mark
expand the bracket: 3m + 24 = 5m + 8.1 mark
rearrange to collect terms: 24 - 8 = 5m - 3m, giving 16 = 2m.1 mark
solve and state the answer, m = 8, so Mia is 8 now (check: in 8 years she is 16 and her uncle, currently 40, is 48; 16 : 48 simplifies to 1 : 3).1 mark

Nothing ticked yet - 5 available

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Free printable worksheet

Want more practice on paper? Download the age and difference problems worksheet pack - 7 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.

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This topic is chapter 28 of 11+ Maths Workbook 4, the whole course as one free printable PDF.

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