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Problems on Ages

Present, past and future age relations.

45 solved questions · 15 easy · 20 medium · 10 hard

Take a 10-question quiz on Problems on Ages, no login

Shortcuts & formulas

  • Age difference between two people never changes with time.
  • If the ratio of ages is a : b now, write the ages as ax and bx, then apply the change (+n or -n years) to each.
  • Age n years ago = present age - n; age n years hence = present age + n.
  • Average age = (sum of ages) / (number of persons); a change in average x group size gives the change in total.
  • Translate words carefully: 'A is twice as old as B' means A = 2B; 'A was twice as old as B 5 years ago' means A - 5 = 2(B - 5).
  • Form linear equations in present ages, solve, and check the answer against every statement.

Solved examples

Try each one first, then open the answer and the step-by-step solution.

Easy questions

Q1.

A father is 3 times as old as his son. The sum of their ages is 48 years. How old is the son?

  1. A12 years
  2. B16 years
  3. C9 years
  4. D24 years
Show answer & solution

Answer: A. 12 years

Solution

Let son = x, father = 3x. x + 3x = 48, so 4x = 48 and x = 12 Answer: 12 years

Q2.

The ages of two friends are in the ratio 4 : 5 and the sum of their ages is 45 years. What is the age of the elder?

  1. A20 years
  2. B25 years
  3. C27 years
  4. D30 years
Show answer & solution

Answer: B. 25 years

Solution

Let ages be 4x and 5x. 9x = 45, so x = 5 Elder = 5 x 5 = 25 years Answer: 25 years

Q3.

Ravi is 8 years older than Asha. If Asha is 17 years old, how old will Ravi be 5 years from now?

  1. A25 years
  2. B22 years
  3. C30 years
  4. D28 years
Show answer & solution

Answer: C. 30 years

Solution

Ravi now = 17 + 8 = 25 years After 5 years = 25 + 5 = 30 years Answer: 30 years

Q4.

Five years ago Meena was 20 years old. How old will she be 7 years from now?

  1. A27 years
  2. B25 years
  3. C30 years
  4. D32 years
Show answer & solution

Answer: D. 32 years

Solution

Present age = 20 + 5 = 25 years Age after 7 years = 25 + 7 = 32 years Answer: 32 years

Q5.

A father is 40 years old and his son is 10 years old. After how many years will the father be twice as old as the son?

  1. A20 years
  2. B15 years
  3. C10 years
  4. D25 years
Show answer & solution

Answer: A. 20 years

Solution

Let it happen after x years. 40 + x = 2 (10 + x) 40 + x = 20 + 2x, so x = 20 Answer: 20 years

Q6.

The average age of three persons is 20 years. If two of them are 18 and 24 years old, how old is the third?

  1. A20 years
  2. B18 years
  3. C16 years
  4. D22 years
Show answer & solution

Answer: B. 18 years

Solution

Sum of ages = 3 x 20 = 60 Sum of two = 18 + 24 = 42 Third person = 60 - 42 = 18 years Answer: 18 years

Q7.

A mother is 4 times as old as her daughter. The difference between their ages is 27 years. How old is the mother?

  1. A27 years
  2. B9 years
  3. C36 years
  4. D45 years
Show answer & solution

Answer: C. 36 years

Solution

Let daughter = x, mother = 4x. 4x - x = 27, so x = 9 Mother = 4 x 9 = 36 years Answer: 36 years

Q8.

A is 5 years older than B and the sum of their ages is 35 years. What is A's age?

  1. A15 years
  2. B25 years
  3. C30 years
  4. D20 years
Show answer & solution

Answer: D. 20 years

Solution

Let B = x, A = x + 5. 2x + 5 = 35, so x = 15 A = 15 + 5 = 20 years Answer: 20 years

Q9.

In 6 years, Meena will be 30 years old. How old was she 4 years ago?

  1. A20 years
  2. B24 years
  3. C26 years
  4. D22 years
Show answer & solution

Answer: A. 20 years

Solution

Present age = 30 - 6 = 24 years 4 years ago = 24 - 4 = 20 years Answer: 20 years

Q10.

The present ages of two brothers are in the ratio 3 : 5 and the difference between their ages is 12 years. What is the age of the younger brother?

  1. A12 years
  2. B18 years
  3. C30 years
  4. D24 years
Show answer & solution

Answer: B. 18 years

Solution

Let ages be 3x and 5x. 5x - 3x = 12, so x = 6 Younger = 3 x 6 = 18 years Answer: 18 years

Q11.

The average age of a family of 4 members is 30 years. What is the total of their ages?

  1. A34 years
  2. B30 years
  3. C120 years
  4. D100 years
Show answer & solution

Answer: C. 120 years

Solution

Total = Average x Number of members = 30 x 4 = 120 years Answer: 120 years

Q12.

A's age is 3 times B's age. If B is 15 years old, what will A's age be 10 years from now?

  1. A45 years
  2. B25 years
  3. C65 years
  4. D55 years
Show answer & solution

Answer: D. 55 years

Solution

A now = 3 x 15 = 45 years After 10 years = 45 + 10 = 55 years Answer: 55 years

Q13.

A father is 28 years older than his son. If the son is 12 years old, how old was the father 4 years ago?

  1. A36 years
  2. B40 years
  3. C32 years
  4. D44 years
Show answer & solution

Answer: A. 36 years

Solution

Father now = 12 + 28 = 40 years 4 years ago = 40 - 4 = 36 years Answer: 36 years

Q14.

The sum of the ages of Ravi and Sita is 30 years and Ravi is 4 years older than Sita. What is Sita's age?

  1. A17 years
  2. B13 years
  3. C15 years
  4. D11 years
Show answer & solution

Answer: B. 13 years

Solution

Let Sita = x, Ravi = x + 4. 2x + 4 = 30, so x = 13 Answer: 13 years

Q15.

Two years ago Arun was 18 years old. How old will he be after 3 years?

  1. A21 years
  2. B25 years
  3. C23 years
  4. D20 years
Show answer & solution

Answer: C. 23 years

Solution

Present age = 18 + 2 = 20 years After 3 years = 20 + 3 = 23 years Answer: 23 years

Medium questions

Q16.

Six years ago, a father was 4 times as old as his son. The sum of their present ages is 52 years. What is the father's present age?

  1. A40 years
  2. B32 years
  3. C36 years
  4. D38 years
Show answer & solution

Answer: D. 38 years

Solution

Let present ages be F and S. F - 6 = 4 (S - 6) and F + S = 52 F = 4S - 18, so 5S - 18 = 52, S = 14 F = 52 - 14 = 38 years Check: 6 years ago F = 32 and S = 8, and 32 = 4 x 8 Answer: 38 years

Q17.

After 5 years, a mother will be 3 times as old as her daughter. The difference between their present ages is 20 years. What is the daughter's present age?

  1. A5 years
  2. B10 years
  3. C15 years
  4. D8 years
Show answer & solution

Answer: A. 5 years

Solution

Let mother = M, daughter = D. M = D + 20 and M + 5 = 3 (D + 5) D + 25 = 3D + 15, so 2D = 10 and D = 5 M = 25; check: after 5 years 30 = 3 x 10 Answer: 5 years

Q18.

The ages of two sisters are in the ratio 3 : 4. After 6 years the ratio will be 4 : 5. What is the present age of the elder sister?

  1. A18 years
  2. B24 years
  3. C30 years
  4. D20 years
Show answer & solution

Answer: B. 24 years

Solution

Let ages be 3x and 4x. (3x + 6)/(4x + 6) = 4/5 15x + 30 = 16x + 24, so x = 6 Elder = 4 x 6 = 24 years Answer: 24 years

Q19.

The present ages of A and B are in the ratio 7 : 9. Eight years ago their ages were in the ratio 3 : 4. What is the sum of their present ages?

  1. A112 years
  2. B96 years
  3. C128 years
  4. D144 years
Show answer & solution

Answer: C. 128 years

Solution

Let ages be 7x and 9x. (7x - 8)/(9x - 8) = 3/4 28x - 32 = 27x - 24, so x = 8 Ages = 56 and 72, sum = 128 years Answer: 128 years

Q20.

The average age of 5 persons is 24 years. When a new person joins them, the average becomes 26 years. What is the age of the new person?

  1. A30 years
  2. B26 years
  3. C34 years
  4. D36 years
Show answer & solution

Answer: D. 36 years

Solution

Total of 5 persons = 5 x 24 = 120 Total of 6 persons = 6 x 26 = 156 New person = 156 - 120 = 36 years Answer: 36 years

Q21.

The average age of 30 students in a class is 14 years. When the teacher's age is included, the average becomes 15 years. What is the teacher's age?

  1. A45 years
  2. B40 years
  3. C44 years
  4. D50 years
Show answer & solution

Answer: A. 45 years

Solution

Total age of students = 30 x 14 = 420 Total with teacher = 31 x 15 = 465 Teacher = 465 - 420 = 45 years Answer: 45 years

Q22.

The average age of a family of 5 members is 24 years. The youngest member is 8 years old. What was the average age of the family just before the youngest member was born?

  1. A22 years
  2. B20 years
  3. C24 years
  4. D18 years
Show answer & solution

Answer: B. 20 years

Solution

Total age now = 5 x 24 = 120 Other 4 members now = 120 - 8 = 112 When the youngest was born (8 years ago) the 4 members were 112 - 4 x 8 = 80 in total Average = 80 / 4 = 20 years Answer: 20 years

Q23.

The ages of three brothers are in the ratio 3 : 5 : 7 and the sum of their ages is 75 years. What is the age of the eldest?

  1. A25 years
  2. B15 years
  3. C35 years
  4. D30 years
Show answer & solution

Answer: C. 35 years

Solution

Let ages be 3x, 5x, 7x. 15x = 75, so x = 5 Eldest = 7 x 5 = 35 years Answer: 35 years

Q24.

Five children were born at intervals of 3 years each. The sum of their present ages is 50 years. What is the age of the eldest child?

  1. A20 years
  2. B14 years
  3. C18 years
  4. D16 years
Show answer & solution

Answer: D. 16 years

Solution

Let the youngest be x. Ages: x, x+3, x+6, x+9, x+12. Sum = 5x + 30 = 50, so x = 4 Eldest = 4 + 12 = 16 years Answer: 16 years

Shortcut: The middle child is the average: 50/5 = 10, so the eldest = 10 + 6 = 16.

Q25.

A father is 24 years older than his son. After 6 years, the father will be twice as old as the son. What is the father's present age?

  1. A42 years
  2. B36 years
  3. C48 years
  4. D30 years
Show answer & solution

Answer: A. 42 years

Solution

Let son = x, father = x + 24. x + 24 + 6 = 2 (x + 6) x + 30 = 2x + 12, so x = 18 Father = 18 + 24 = 42 years Answer: 42 years

Q26.

A is twice as old as B. Four years ago, A was 3 times as old as B was then. What is A's present age?

  1. A12 years
  2. B16 years
  3. C20 years
  4. D8 years
Show answer & solution

Answer: B. 16 years

Solution

Let B = x, A = 2x. 2x - 4 = 3 (x - 4) 2x - 4 = 3x - 12, so x = 8 A = 16 years Check: 4 years ago A = 12 and B = 4, and 12 = 3 x 4 Answer: 16 years

Q27.

The sum of the present ages of A and B is 50 years. Five years ago, the ratio of their ages was 3 : 2. What is A's present age?

  1. A30 years
  2. B25 years
  3. C29 years
  4. D32 years
Show answer & solution

Answer: C. 29 years

Solution

Let A = a, B = 50 - a. (a - 5)/(45 - a) = 3/2 2a - 10 = 135 - 3a, so 5a = 145 and a = 29 Answer: 29 years

Q28.

The present ages of A and B are in the ratio 5 : 3. Four years ago the ratio was 3 : 1. What will be B's age after 10 years?

  1. A10 years
  2. B12 years
  3. C20 years
  4. D16 years
Show answer & solution

Answer: D. 16 years

Solution

Let ages be 5x and 3x. (5x - 4)/(3x - 4) = 3/1 5x - 4 = 9x - 12, so x = 2 A = 10, B = 6 B after 10 years = 6 + 10 = 16 years Answer: 16 years

Q29.

A father is 3 times as old as his son. After 12 years, he will be twice as old as his son. What is the father's present age?

  1. A36 years
  2. B24 years
  3. C48 years
  4. D30 years
Show answer & solution

Answer: A. 36 years

Solution

Let son = x, father = 3x. 3x + 12 = 2 (x + 12) 3x + 12 = 2x + 24, so x = 12 Father = 36 years Answer: 36 years

Q30.

The average age of 8 persons is 28 years. A person aged 44 years leaves the group and is replaced by a person aged 20 years. What is the new average age?

  1. A26 years
  2. B25 years
  3. C27 years
  4. D24 years
Show answer & solution

Answer: B. 25 years

Solution

Original total = 8 x 28 = 224 New total = 224 - 44 + 20 = 200 New average = 200 / 8 = 25 years Answer: 25 years

Q31.

Ravi is 6 years older than Meena. Four years ago the ratio of their ages was 5 : 4. What is Meena's present age?

  1. A30 years
  2. B24 years
  3. C28 years
  4. D34 years
Show answer & solution

Answer: C. 28 years

Solution

Let Meena = m, Ravi = m + 6. (m + 6 - 4)/(m - 4) = 5/4 4m + 8 = 5m - 20, so m = 28 Check: 4 years ago Ravi = 30, Meena = 24; 30 : 24 = 5 : 4 Answer: 28 years

Q32.

A's age after 10 years will be twice B's age 10 years ago. If A is 9 years older than B, what is B's present age?

  1. A29 years
  2. B48 years
  3. C49 years
  4. D39 years
Show answer & solution

Answer: D. 39 years

Solution

Let B = b, A = b + 9. b + 9 + 10 = 2 (b - 10) b + 19 = 2b - 20, so b = 39 years Check: A = 48; after 10 years 58 = 2 x 29 (B 10 years ago) Answer: 39 years

Q33.

The total of the ages of three persons 10 years ago was 54 years. What will be the total of their ages 5 years from now?

  1. A99 years
  2. B84 years
  3. C69 years
  4. D89 years
Show answer & solution

Answer: A. 99 years

Solution

Total 10 years ago = 54 Each person has aged 10 + 5 = 15 years, so for three persons: 3 x 15 = 45 Total after 5 years = 54 + 45 = 99 years Answer: 99 years

Q34.

Rohit is 3 times as old as Sohan. After 5 years he will be twice as old as Sohan. After how many years from now will the sum of their ages be 60?

  1. A15 years
  2. B20 years
  3. C25 years
  4. D10 years
Show answer & solution

Answer: B. 20 years

Solution

Let Sohan = x, Rohit = 3x. 3x + 5 = 2 (x + 5), so x = 5 and Rohit = 15 Sum now = 15 + 5 = 20 Each year the sum increases by 2 (both age by 1) Years needed = (60 - 20)/2 = 20 Answer: 20 years

Q35.

Ages of A and B are in the ratio 5 : 6. After 8 years the ratio will be 7 : 8. What is B's present age?

  1. A20 years
  2. B28 years
  3. C24 years
  4. D30 years
Show answer & solution

Answer: C. 24 years

Solution

Let ages be 5x and 6x. (5x + 8)/(6x + 8) = 7/8 40x + 64 = 42x + 56, so x = 4 B = 6 x 4 = 24 years Answer: 24 years

Hard questions

Q36.

Ravi is twice as old as Sita was when Ravi was as old as Sita is now. If the sum of their present ages is 56 years, how old is Ravi?

  1. A24 years
  2. B28 years
  3. C36 years
  4. D32 years
Show answer & solution

Answer: D. 32 years

Solution

Let Ravi = R, Sita = S (R > S). The gap is R - S years. When Ravi was S years old (R - S years ago), Sita was S - (R - S) = 2S - R. R = 2 (2S - R), so 3R = 4S and R : S = 4 : 3 R + S = 56, so R = 32 and S = 24 Check: 8 years ago Ravi was 24 and Sita 16; 32 = 2 x 16 Answer: 32 years

Q37.

The ages of A and B are in the ratio 5 : 7. After 6 years the ratio of their ages will be 3 : 4. What is B's present age?

  1. A42 years
  2. B30 years
  3. C35 years
  4. D48 years
Show answer & solution

Answer: A. 42 years

Solution

Let ages be 5x and 7x. (5x + 6)/(7x + 6) = 3/4 20x + 24 = 21x + 18, so x = 6 B = 7 x 6 = 42 years Check: after 6 years 36 : 48 = 3 : 4 Answer: 42 years

Q38.

The present ages of three persons are in the ratio 4 : 7 : 9. Eight years ago, the sum of their ages was 56 years. What is the age of the youngest person now?

  1. A12 years
  2. B16 years
  3. C20 years
  4. D28 years
Show answer & solution

Answer: B. 16 years

Solution

Let ages be 4x, 7x, 9x. Eight years ago the sum = 20x - 3 x 8 = 20x - 24 20x - 24 = 56, so x = 4 Youngest = 4 x 4 = 16 years Answer: 16 years

Q39.

A father's age is 3 years more than 3 times his son's age. Three years from now, the father's age will be 10 years more than twice the son's age. What is the father's present age?

  1. A30 years
  2. B36 years
  3. C33 years
  4. D43 years
Show answer & solution

Answer: C. 33 years

Solution

Let son = s, father = 3s + 3. After 3 years: 3s + 6 = 2 (s + 3) + 10 3s + 6 = 2s + 16, so s = 10 Father = 3 x 10 + 3 = 33 years Answer: 33 years

Q40.

A mother was 28 years old when her first child was born and 32 years old when her second child was born. At present the sum of the ages of the two children equals the mother's age. How old is the mother?

  1. A56 years
  2. B64 years
  3. C48 years
  4. D60 years
Show answer & solution

Answer: D. 60 years

Solution

Let mother's present age = M. First child = M - 28, second child = M - 32 M = (M - 28) + (M - 32) = 2M - 60, so M = 60 years Children are 32 and 28 years old: 32 + 28 = 60 Answer: 60 years

Q41.

The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 4 times the father's age at that time. What is the father's present age?

  1. A36 years
  2. B34 years
  3. C39 years
  4. D40 years
Show answer & solution

Answer: A. 36 years

Solution

Let father = f, son = s. f + s = 45. Five years ago: (f - 5)(s - 5) = 4 (f - 5) Divide by (f - 5): s - 5 = 4, so s = 9 f = 45 - 9 = 36 years Answer: 36 years

Q42.

A woman says, 'I am 4 times as old as my son. After 5 years I will be 3 times as old as he will be then.' How old will her son be 20 years from now?

  1. A10 years
  2. B30 years
  3. C15 years
  4. D25 years
Show answer & solution

Answer: B. 30 years

Solution

Let son = s, woman = 4s. 4s + 5 = 3 (s + 5), so s = 10 and she is 40 Son after 20 years = 10 + 20 = 30 years Answer: 30 years

Q43.

A father is 30 years older than his son. Five years ago the father's age was 4 times the son's age. After how many years from now will the father be twice as old as the son?

  1. A10 years
  2. B20 years
  3. C15 years
  4. D5 years
Show answer & solution

Answer: C. 15 years

Solution

Let son = s, father = s + 30. s + 25 = 4 (s - 5), so 3s = 45 and s = 15; father = 45 Let it happen after x years: 45 + x = 2 (15 + x) 45 + x = 30 + 2x, so x = 15 Answer: 15 years

Q44.

Three years ago the ratio of the ages of A and B was 3 : 4. Three years from now it will be 5 : 6. What is the sum of their present ages?

  1. A30 years
  2. B24 years
  3. C33 years
  4. D27 years
Show answer & solution

Answer: D. 27 years

Solution

Let present ages be a and b. (a - 3)/(b - 3) = 3/4 gives 4a = 3b + 3 (a + 3)/(b + 3) = 5/6 gives 6a = 5b - 3 From the first, a = (3b + 3)/4; put in the second: 6 (3b + 3)/4 = 5b - 3 18b + 18 = 20b - 12, so b = 15 and a = 12 Sum = 27 years Answer: 27 years

Q45.

A is 2 years older than B, and B is twice as old as C. If the sum of the ages of A, B and C is 27 years, how old is B?

  1. A10 years
  2. B8 years
  3. C12 years
  4. D14 years
Show answer & solution

Answer: A. 10 years

Solution

Let C = x, B = 2x, A = 2x + 2. x + 2x + 2x + 2 = 27, so 5x = 25 and x = 5 B = 2 x 5 = 10 years Check: A = 12, B = 10, C = 5; sum = 27 Answer: 10 years

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