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Age puzzles

Everyone gets older at the same speed. Use that to solve puzzles about ages now, years ago and years from now.

Age puzzles have been in school books for hundreds of years. They look hard because they jump between the past, the present and the future. But they all rest on one simple fact: everyone gets older at the same speed. In one year, a baby gets one year older, and so does her grandmother. Once you use that fact, and always find the ages now first, these puzzles become short and clear.

Find the age now first

Many puzzles tell you an age in the future or in the past and ask about a different time. Do not jump straight from one to the other. Go through today.

  • "In 5 years" means add 5 to the age now. So to get back to now, take 5 away.
  • "5 years ago" means take 5 away from the age now. So to get back to now, add 5.

Example 1

In 4 years, Mia will be 15. How old was Mia 3 years ago?

  1. Now: 15 − 4 = 11.
  2. 3 years ago: 11 − 3 = 8.

Answer: 8

The difference never changes

Ana is 7 and Ben is 3. Ana is 4 years older. Next year they will be 8 and 4, and Ana is still 4 years older. In 20 years they will be 27 and 23: still 4 years. Because both get older at the same speed, the difference between two ages is the same for their whole lives.

Remember

The difference between two people's ages is always the same.

TimeAnaBenDifference
now734
in 5 years1284
in 13 years20164

Example 2

Sam is 9 and his father is 37. When Sam is 25, how old will his father be?

  1. The difference is 37 − 9 = 28 years.
  2. It never changes, so when Sam is 25, his father is 25 + 28 = 53.
  3. Check: Sam gets 25 − 9 = 16 years older, and so does his father: 37 + 16 = 53.

Answer: 53

The total and the difference

Some puzzles give the total of two ages and the difference between them. Take the difference away from the total. What is left is the younger age twice, so divide by 2.

Remember

Younger age = (total − difference) ÷ 2

The older age is then the younger age plus the difference.

Example 3

Two sisters are 26 years old in total. One is 8 years older than the other. How old is the younger sister?

  1. Take away the older sister's 8 extra years: 26 − 8 = 18.
  2. Now the two ages are equal, so each is 18 ÷ 2 = 9.
  3. The younger sister is 9, and the older one is 9 + 8 = 17.
  4. Check: 9 + 17 = 26 and 17 − 9 = 8.

Answer: 9

Times as old: count in parts

When one age is a number of times another, think of the younger age as one part. If a mother is 4 times as old as her son, her age is 4 parts. The difference between them is 4 − 1 = 3 parts. If you know the difference in years, you can find one part.

Example 4

A grandfather is 60 years older than his grandson. He is 5 times as old as the grandson. How old is the grandson?

  1. The grandson is 1 part and the grandfather is 5 parts.
  2. The difference is 5 − 1 = 4 parts, and it is 60 years.
  3. One part: 60 ÷ 4 = 15. So the grandson is 15.
  4. Check: the grandfather is 5 × 15 = 75, and 75 − 15 = 60.

Answer: 15

Harder puzzles: two times at once

The hardest puzzles compare ages at two different times. Two ideas solve them: the difference never changes, and you can always check an answer by putting it back into the story.

Example 5

In 6 years, Lea will be 3 times as old as she was 6 years ago. How old is Lea now?

  1. From "6 years ago" to "in 6 years" is 12 years. So her age then and her age later differ by 12.
  2. Her later age is 3 parts and her earlier age is 1 part, so the difference is 2 parts.
  3. 2 parts are 12 years, so 1 part is 6. Six years ago, Lea was 6.
  4. Now she is 6 + 6 = 12.
  5. Check: in 6 years she will be 18, and 6 years ago she was 6. 18 is 3 times 6.

Answer: 12

Example 6

A mother is 3 times as old as her daughter. In 12 years, she will be twice as old as her daughter. How old is the daughter now?

  1. Now: the daughter is 1 part and the mother is 3 parts, so the difference is 2 parts, or twice the daughter's age.
  2. In 12 years the mother is twice the daughter's age, so the difference is the daughter's age then: her age now plus 12.
  3. The difference never changes, so twice her age now equals her age now plus 12.
  4. Take her age now from both sides: her age now is 12.
  5. Check: the mother is 36. In 12 years they are 24 and 48, and 48 is twice 24.

Answer: 12

Try it yourself

  1. 1.6 years ago, Omar was 9. How old will he be in 4 years?

    Show the answer

    19

    Now he is 9 + 6 = 15. In 4 years he will be 15 + 4 = 19.

  2. 2.Lily is 4 and her brother is 11. When Lily is 30, how old will her brother be?

    Show the answer

    37

    He is always 11 − 4 = 7 years older, and 30 + 7 = 37.

  3. 3.Two cousins are 40 years old in total. One is 10 years older than the other. How old is the younger cousin?

    Show the answer

    15

    40 − 10 = 30, and half of that is 15. The older cousin is 25.

  4. 4.A father is 24 years older than his son and 3 times as old. How old is the son?

    Show the answer

    12

    The difference is 3 − 1 = 2 parts, and 2 parts are 24 years, so one part is 12. The father is 36.

  5. 5.In 4 years, Kim will be twice as old as she was 4 years ago. How old is Kim now?

    Show the answer

    12

    Her two ages differ by 8 years, and "twice" means the difference is 1 part. So 4 years ago she was 8, and now she is 12. Check: 16 is twice 8.

Ready to test yourself?

Play Logic: 20 seconds per question, and it gets harder as you go.