Problems on ages for SSC GD

Age problems give people's ages now, in the past or in the future. The wording can feel like a riddle, but the maths is simple. Almost every question becomes one small equation, and many can be solved by trying the four options.

Two facts make this whole chapter easy:

1. Everyone gets older by the same number of years. In 5 years, every person in the question is 5 years older.
2. The difference between two people's ages never changes. If one person is 12 years older today, they were 12 years older ten years ago and will be 12 years older in twenty years.

Method 1: set up an equation

1. Let the younger or smaller age be x (or use ratio parts, such as 3x and 4x).
2. Write the other age in terms of x.
3. Move both ages to the time the question talks about: add years for the future, subtract for the past.
4. Write the condition as an equation and solve.
5. Check the answer against every sentence of the question.

Method 2: test the options

SSC GD gives four options, and trying them is often faster than algebra. Put each option into the conditions one by one. The right option passes all of them; a wrong one usually fails the first check.

Solved examples

Example 1. A parent is 4 times as old as their child. In 20 years, the parent will be twice as old as the child. Find their present ages.

1. Let the child's age be x. The parent is 4x.
2. In 20 years: 4x + 20 = 2(x + 20).
3. 4x + 20 = 2x + 40, so 2x = 20 and x = 10.
4. Child = 10 years; parent = 40 years.
5. Check: in 20 years they are 30 and 60, and 60 is twice 30.

Example 2. The sum of the ages of a parent and a child is 50. Five years ago, the parent was 4 times as old as the child. Options: (a) 40, 10 (b) 37, 13 (c) 35, 15 (d) 42, 8.

1. All options add to 50, so the sum does not help.
2. Test (a): five years ago, 35 and 5. 35 is 7 times 5. Wrong.
3. Test (b): five years ago, 32 and 8. 32 is 4 times 8. Right.
4. Answer: (b) 37 and 13.

Example 3. The ages of two siblings are in the ratio 2 : 3. The elder is 6 years older. Find their ages.

1. Ages are 2x and 3x. The difference is 1 part, so x = 6.
2. Ages: 12 and 18.

Example 4. The ratio of the ages of A and B is 3 : 4. After 5 years, it will be 4 : 5. Find their present ages.

1. Ages are 3x and 4x. After 5 years: (3x + 5)/(4x + 5) = 4/5.
2. Cross-multiply: 15x + 25 = 16x + 20, so x = 5.
3. Ages: 15 and 20. Check: after 5 years, 20 : 25 = 4 : 5.

Example 5. Ten years ago, A was twice as old as B. Today A is 12 years older than B. Find their present ages.

1. The difference is always 12. Ten years ago, A = 2 × B and A − B = 12, so B was 12 and A was 24.
2. Today: A = 34, B = 22.

Example 6. The average age of 4 friends is 20 years. When a fifth friend joins, the average becomes 21. How old is the fifth friend?

1. Total of 4 ages = 4 × 20 = 80.
2. Total of 5 ages = 5 × 21 = 105.
3. Fifth friend = 105 − 80 = 25 years.

For more on totals and averages, see average.

A shortcut for ratio questions

In Example 4, the ratio moves from 3 : 4 to 4 : 5. Both ratios have a difference of 1 part, so the part size stays the same, and the 5 years added equal 1 part. That gives x = 5 at once. Use this only when the part differences match; otherwise use the equation. Ratio covers parts in more detail.

Common mistakes

Practice set

1. A parent is 3 times as old as their child. After 12 years, the parent will be twice as old. Find the child's present age.
2. The sum of two siblings' ages is 30, and the elder is 6 years older. Find their ages.
3. The ratio of the ages of X and Y is 5 : 7. The sum of their ages is 48. Find their ages.
4. Five years ago, a person was 20. How old will the person be in 10 years?
5. The ratio of the ages of A and B is 4 : 5. Eight years ago, it was 2 : 3. Find their present ages.
6. The average age of 3 children is 12. When a teacher is included, the average becomes 17. Find the teacher's age.
7. A is twice as old as B. Five years ago, A was three times as old as B. Find their present ages.
8. A grandparent is 60 and a grandchild is 12. After how many years will the grandparent be three times as old as the grandchild?

Answers:

1. Child x, parent 3x. 3x + 12 = 2(x + 12), so x = 12 years (parent 36; in 12 years, 48 and 24).
2. Younger = (30 − 6) ÷ 2 = 12. Ages 18 and 12.
3. 12 parts = 48, so 1 part = 4. Ages 20 and 28.
4. Now 25, so in 10 years 35.
5. (4x − 8)/(5x − 8) = 2/3 gives 12x − 24 = 10x − 16, so x = 4. Ages 16 and 20 (eight years ago 8 and 12).
6. 4 × 17 − 3 × 12 = 68 − 36 = 32 years.
7. 2x − 5 = 3(x − 5) gives x = 10. A 20, B 10 (five years ago 15 and 5).
8. 60 + n = 3(12 + n) gives 60 + n = 36 + 3n, so n = 12 years (then 72 and 24).

What to do next

• Solve ten age questions by algebra, then solve the same ten by testing options, and compare your time.
• Practise five ratio-change questions using the parts shortcut.
• Mix three age questions into every maths mock you take this week.