Quantitative Aptitude

Problems on Ages

346 Questions

Problems on Ages involve calculating current, past, or future ages using ratios, averages, and simple equations. These questions are a regular feature in the arithmetic section of most competitive exams. Practicing these problems helps improve calculation speed and accuracy for time management during tests.

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Problems on Ages Questions

Multiple choice

The sum of the ages of a father and his son is 40 years. Four years ago, the father's age was 3 times his son's age. What is the present age of the father?

  1. 28 years

  2. 32 years

  3. 30 years

  4. 25 years

  5. 20 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the present age of father be x years. So, present age of son = 40 - x years Four years ago, age of father = x - 4 years and age of son = 40 - x - 4 = 36 - x years Now, according to question, x - 4 = 3(36 - x) On solving this equation, we get x = 28 years So, the present age of father is 28 years.

Multiple choice

A is 5 years older than B, who is 2 years older than half of age of C. If the average age of A, B and C is 59 years, then find the age of B after 6 years.

  1. 50 years

  2. 44 years

  3. 60 years

  4. 54 years

  5. 40 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the present age of A be x years.

Then, present age of B = x - 5 years and that of C = 2(x - 5 - 2) = 2x - 14 years 

So, average of A, B and C = 59 years 

(x + x - 5 + 2x - 14)/3 = 59

x = 49

So, the present age of A is 49 years.

Then present age of B = 49 - 5 => 44 years 

Therefore B's age after 6 years = 44 + 6 => 50 years.

Multiple choice

The age of a father, 9 years ago, was 4 times the age of his son. Nine years hence, the age of the father will be twice that of his son. Find the present age of the father.

  1. 40 years

  2. 42 years

  3. 47 years

  4. 45 years

  5. 50 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the present age of father be x years and that of the son be y years.

Then, 9 years ago, father's age = x - 9 and son's age = y - 9 years

So, according to question,

x - 9 = 4 (y - 9) 

x - 4y = -27 ------------------(1)

Now, 9 years hence, father's age = x + 9 years and son's age = y + 9 years

Again, x + 9 = 2(y + 9)

x - 2y = 9 -------------------------(2)

On solving the equations (1) and (2), we get

x = 45 and y = 18

So, the present age of father is 45 years.

Multiple choice

Five years ago, the average age of A and B was 11 years. After adding the age of C to the ages of A and B, the average remained the same. How old is C now?

  1. 14 years

  2. 18 years

  3. 11 years

  4. 16 years

  5. 13 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Five years ago, average age of A and B = 11 years So, sum of ages of A and B, 5 years ago = 11 x 2 = 22 years On adding the age of C, average age of A, B and C = 11 years So, (22 + C)/3 = 11 22 + C = 33 C = 11 Therefore, 5 years ago, C's age was 11 years. So, present age of C = 11 + 5 = 16 years

Multiple choice

The difference of the ages of a father and his son is 18 years. After 6 years, the sum of their ages will be 54 years. Find the product of their ages 10 years ago.

  1. 40 years2

  2. 36 years2

  3. 39 years2

  4. 38 years2

  5. 50 years2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the present age of son be x years. Then, present age of father = (x + 18) years After 6 years, son's age = (x + 6) years and father's age = (x + 18 + 6) years = (x + 24) years Now, according to question, (x + 6) + (x + 24) = 54 2x + 30 = 54 x = 12 So, present age of son = 12 years and present age of father = 12 + 18 = 30 years Ten years ago, father's age = 30 - 10 = 20 years and son's age = 12 - 10 = 2 years Now, product of their ages = 20 years x 2 years= 40 years2

Multiple choice

Five years ago, a mother's age was 15 times that of her daughter. After 5 years, the mother's age will be 10/3 times her daughter's age. Find the present age of the daughter.

  1. 7 years

  2. 10 years

  3. 12 years

  4. 13 years

  5. 8 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let five years ago, daughter's age = x years and mother's age = 15x years Now, after 5 years, daughter's age = x + 5 + 5 = x + 10 years and mother's age = 15x + 5 + 5 = 15x + 10 years Now, according to question, 10/3(x + 10) = 15x + 10 x = 2 So, present age of daughter = 2 + 5 = 7 years

Multiple choice

Kavita got married 20 years ago. Today, her age is 19/9 times of her age at the time of marriage. Her son's age is half her age. What is the present age of her son?

  1. 12 years

  2. 13 years

  3. 14 years

  4. 19 years

  5. 15 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the present age of son be x years. Then, present age of Kavita = 2x years Twenty years ago, Kavita's age = 2x - 20 years Now, according to question, 19/9(2x - 20) = 2x After solving the above equation, we get x = 19 So, the present age of son is 19 years.

Multiple choice

Two years ago, the ratio of ages of A and B was 10 : 9. Six years hence, the ratio of their ages will be 14 : 13. Find the present age of B.

  1. 29 years

  2. 38 years

  3. 20 years

  4. 47 years

  5. 11 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A's age 2 years ago be 10x years and that of B be 9x years. So, 6 years hence, age of A = 10x + 2 + 6 = 10x + 8 years and age of B = 9x + 2 + 6 = 9x + 8 years Now, according to question, (10x + 8)/(9x + 8) = 14/13 After solving this equation, we get x = 2 So, present age of B = 9x + 2 = 9 x 2 + 2 => 20 years

Multiple choice

The ratio of Lila's age and her daughter's age is 7 : 4. The difference of their ages is 18 years. Find the ratio of their ages after 6 years.

  1. 5 : 3

  2. 4 : 3

  3. 3 : 2

  4. 6 : 5

  5. 5 : 4
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the present age of Lila be 7x years and that of her daughter be 4x years. Now, according to question, 7x - 4x = 18 x = 3 So, present age of Lila = 7 x 3 = 21 years and that of her daughter = 4 x 3 = 12 years Now, age of Lila after 6 years = 21 + 6 = 27 years and that of her daughter = 12 + 6 = 18 years So, ratio their ages after 6 years = 27 : 18 = 3 : 2

Multiple choice

Ten years ago, A's age was 1/5 of B's age. If the ratio of their present ages is 3 : 5, what is the sum of their present ages?

  1. 16 years

  2. 24 years

  3. 40 years

  4. 32 years

  5. 48 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the present age of A be 3x years and that of B be 5x years. 10 years ago, A's age = 3x -10 and B's age = 5x - 10 years Now, according to question, 3x - 10 = 1/5(5x - 10) After solving this equation, we get x = 4 So, sum of ages of A and B = 3 x 4 + 5 x 4 = 32 years

Multiple choice

The age of a man is 3 times that of his son. Ten years ago, the man was 8 times as old as his son was at that time. Find the present age of the man.

  1. 36 years

  2. 39 years

  3. 48 years

  4. 42 years

  5. 45 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the present age of son be x years. Then, present age of man = 3x years 10 years ago, son's age = x - 10 years and man's age = 3x - 10 years Now, according to question, 8(x - 10) = 3x - 10 x = 14 So, present age of son = 14 years Therefore, present age of man = 14 x 3 = 42 years

Multiple choice

The present age of a father is 1 year more than 4 times the age of his son. One year later, the father's age will 6 years more than thrice the age of his son. What is the present age of the father?

  1. 33 years

  2. 29 years

  3. 45 years

  4. 41 years

  5. 37 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the present age of son be x years and that of father be 4x + 1 years. After 1 year, son's age = x + 1 years and father's age = 4x + 1 + 1 = 4x + 2 years Now, according to question, 3(x + 1) + 6 = 4x + 2 x = 7 So, present age of father = 4 x 7 + 1 = 29 years

Multiple choice

In a family, the average age of 3 sons is 12 years. The average age of the family including the sons, mother and father is 22.8 years. If the father is 6 years older than the mother, then what is the present age of the mother?

  1. 42 years

  2. 36 years

  3. 45 years

  4. 38 years

  5. 32 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the present age of mother be x years. So, age of father = x + 6 years The average age of 3 sons is 12 years. Therefore, sum of the ages of 3 sons = 3 x 12 = 36 years Now, according to question, (36 + x + 6 + x)/5 = 22.8 x = 36 years So, the present age of mother is 36 years.