Worked solutions: Age Problems

All 6 problems from "Age Problems" with complete step-by-step worked solutions: recognising the type, the idea, the working steps and the conclusion. Use this page to review with your child after the animated lesson, or let them check their own working against it.

Every problem, fully solved

In 5 years, a mother and her son will be 50 years old in total. The mother is 30 years older than the son. How old is the son now?

Key idea: The age gap never changes — solve in the future year, then step back.

Recognise

In 5 years a mother and son will total 50, and the mother is 30 years older.

The idea

In 5 years it is a plain sum–difference problem; subtract 5 at the end to come back to today.

Steps

1
Son in 5 years: (50 − 30) ÷ 2 = 10.
2
Son now: 10 − 5 = 5.

So: So the son is 5 years old now.

In 3 years, the total age of a father and daughter will be 38. The father is 20 years older. How old is the father now?

Key idea: The age gap never changes — solve in the future year, then step back.

Recognise

In 3 years a father and daughter will total 38, and the father is 20 years older.

The idea

Sum–difference in the future year first, then step back 3 years.

Steps

1
Daughter in 3 years: (38 − 20) ÷ 2 = 9.
2
Father in 3 years: 9 + 20 = 29.
3
Father now: 29 − 3 = 26.

So: So the father is 26 years old now.

A father is 24 years older than his child. In 5 years, how many years older will the father be?

29 years
24 years
34 years
19 years

Key idea: The age gap NEVER changes — both people gain the same years.

Recognise

A father is 24 years older than his child — how much older will he be in 5 years?

The idea

Both the father and the child gain 5 years, so the gap cannot move.

Steps

1
The father gains 5 years.
2
The child also gains 5 years.
3
Gaining the same amount leaves the difference unchanged.

So: So the father will still be 24 years older.

In 6 years, a grandfather and grandson will total 60 years. The grandfather is 28 years older. The grandson is now ___ years old and the grandfather is now ___ years old.

Key idea: The age gap never changes — solve in the future year, then step back.

Recognise

In 6 years a grandfather and grandson will total 60, and the grandfather is 28 years older.

The idea

Sum–difference in the future year for both, then subtract 6 from each.

Steps

1
Grandson in 6 years: (60 − 28) ÷ 2 = 16, so now 16 − 6 = 10.
2
Grandfather in 6 years: 16 + 28 = 44, so now 44 − 6 = 38.
3
Check: 10 + 38 = 48 today, and 48 + 2 × 6 = 60 in 6 years.

So: So the grandson is now 10 years old and the grandfather is now 38 years old.

Today, a father and son total 28 years and the father is 12 years older. In how many years will their total be 40?

Key idea: A shared total grows by 2 per year — one year for EACH person.

Recognise

A father and son total 28 today; in how many years will their total be 40?

The idea

The total must grow by 12 years, and two people aging add 2 to the total each year.

Steps

1
Growth needed: 40 − 28 = 12 years.
2
Each year the total grows by 2 (father +1 and son +1).
3
12 ÷ 2 = 6 years.

So: So their total will be 40 in 6 years.

In 4 years, a mother and daughter will total 52 years. The mother is 26 years older. How old are they now?

9 and 35
13 and 39
11 and 37
7 and 33

Key idea: The age gap never changes — solve in the future year, then step back.

Recognise

In 4 years a mother and daughter will total 52, and the mother is 26 years older.

The idea

Sum–difference in the future year, then subtract 4 from both ages.

Steps

1
In 4 years: daughter (52 − 26) ÷ 2 = 13, mother 13 + 26 = 39.
2
Today: daughter 13 − 4 = 9, mother 39 − 4 = 35.
3
Check: 9 + 35 = 44, and 44 + 2 × 4 = 52.

So: So they are now 9 and 35.

Learn it with the animated lesson

The problem

In 4 years, a father and child will be 44 years old in total. The father is 24 years older than the child. How old is each person now?

Progress

NaN%

Shortcuts: Space (play), Arrow keys (step), R (reset), F (fullscreen)

Problem overview

A Problem Set in the Future

Now: father ? years, child ? years

In 4 years, a father and child will be 44 years old in total. The father is always 24 years older. How old is each person now?

Key idea

We do not know the ages now — but we know the total in the future. Let us travel there.

Solution steps

0 / 7 steps

Try Your Own Numbers

Sandbox

Change the numbers and watch the diagram redraw itself:

Total age in the future

Age difference

Years later

Practise this type Age Problems

Every problem, fully solved

In 5 years, a mother and her son will be 50 years old in total. The mother is 30 years older than the son. How old is the son now?

Key idea: The age gap never changes — solve in the future year, then step back.

Recognise

In 5 years a mother and son will total 50, and the mother is 30 years older.

The idea

In 5 years it is a plain sum–difference problem; subtract 5 at the end to come back to today.

Steps

1
Son in 5 years: (50 − 30) ÷ 2 = 10.
2
Son now: 10 − 5 = 5.

So: So the son is 5 years old now.

In 3 years, the total age of a father and daughter will be 38. The father is 20 years older. How old is the father now?

Key idea: The age gap never changes — solve in the future year, then step back.

Recognise

In 3 years a father and daughter will total 38, and the father is 20 years older.

The idea

Sum–difference in the future year first, then step back 3 years.

Steps

1
Daughter in 3 years: (38 − 20) ÷ 2 = 9.
2
Father in 3 years: 9 + 20 = 29.
3
Father now: 29 − 3 = 26.

So: So the father is 26 years old now.

A father is 24 years older than his child. In 5 years, how many years older will the father be?

29 years
24 years
34 years
19 years

Key idea: The age gap NEVER changes — both people gain the same years.

Recognise

A father is 24 years older than his child — how much older will he be in 5 years?

The idea

Both the father and the child gain 5 years, so the gap cannot move.

Steps

1
The father gains 5 years.
2
The child also gains 5 years.
3
Gaining the same amount leaves the difference unchanged.

So: So the father will still be 24 years older.

In 6 years, a grandfather and grandson will total 60 years. The grandfather is 28 years older. The grandson is now ___ years old and the grandfather is now ___ years old.

Key idea: The age gap never changes — solve in the future year, then step back.

Recognise

In 6 years a grandfather and grandson will total 60, and the grandfather is 28 years older.

The idea

Sum–difference in the future year for both, then subtract 6 from each.

Steps

1
Grandson in 6 years: (60 − 28) ÷ 2 = 16, so now 16 − 6 = 10.
2
Grandfather in 6 years: 16 + 28 = 44, so now 44 − 6 = 38.
3
Check: 10 + 38 = 48 today, and 48 + 2 × 6 = 60 in 6 years.

So: So the grandson is now 10 years old and the grandfather is now 38 years old.

Today, a father and son total 28 years and the father is 12 years older. In how many years will their total be 40?

Key idea: A shared total grows by 2 per year — one year for EACH person.

Recognise

A father and son total 28 today; in how many years will their total be 40?

The idea

The total must grow by 12 years, and two people aging add 2 to the total each year.

Steps

1
Growth needed: 40 − 28 = 12 years.
2
Each year the total grows by 2 (father +1 and son +1).
3
12 ÷ 2 = 6 years.

So: So their total will be 40 in 6 years.

In 4 years, a mother and daughter will total 52 years. The mother is 26 years older. How old are they now?

9 and 35
13 and 39
11 and 37
7 and 33

Key idea: The age gap never changes — solve in the future year, then step back.

Recognise

In 4 years a mother and daughter will total 52, and the mother is 26 years older.

The idea

Sum–difference in the future year, then subtract 4 from both ages.

Steps

1
In 4 years: daughter (52 − 26) ÷ 2 = 13, mother 13 + 26 = 39.
2
Today: daughter 13 − 4 = 9, mother 39 − 4 = 35.
3
Check: 9 + 35 = 44, and 44 + 2 × 4 = 52.

So: So they are now 9 and 35.

Learn it with the animated lesson

The problem

In 4 years, a father and child will be 44 years old in total. The father is 24 years older than the child. How old is each person now?

Progress

NaN%

Shortcuts: Space (play), Arrow keys (step), R (reset), F (fullscreen)

Problem overview

A Problem Set in the Future

Now: father ? years, child ? years

In 4 years, a father and child will be 44 years old in total. The father is always 24 years older. How old is each person now?

Key idea

We do not know the ages now — but we know the total in the future. Let us travel there.

Solution steps

0 / 7 steps

Try Your Own Numbers

Sandbox

Change the numbers and watch the diagram redraw itself:

Total age in the future

Age difference

Years later