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 average age of 41 students of a class is 15 years. When one boy leaves the class, the average is reduced by 0.05 year. Find the age of the boy who left the class.

  1. 13 years

  2. 14 years

  3. 17 years

  4. 16 years

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

Original average age (A) = 15 years

Original number of students (N) = 41

Difference in average ages (d) = 0.05 years

Now, apply the shortcut formula:

Age of the boy who left the class = A - (1 - N)d 

= 15 - (1 - 41) * 0.05 

= 17 years 

So, the age of the boy who left the class was 17 years.

Multiple choice

The average age of A and B is 24 years. If C were to replace A, the new average of B and C would become 23.5 years and if C were to replace B, then average age would be 22.5 years. What is the age of C?

  1. 22 years

  2. 21 years

  3. 26 years

  4. 20 years

  5. 24 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Average of A and B = 24 years

So, (A + B)/2 = 24

A + B = 48    -------------(1)

On replacing A with C,

(C + B)/2 = 23.5

C + B = 47   -------------(2)

On putting the value of B in equation (2), we get

C + 48 - A = 47

C - A = -1    ---------------(3)

Now, replacing B with C

(A + C)/2 = 22.5

A + C = 45 --------------(4) 

Now, on solving equations (3) and (4), we get

C = 22 years

Multiple choice

The average age of a family of 9 members is 26 years. If the youngest member of the family is 10 years old, then find the average age of the family members at the time of birth of the youngest member.

  1. 18 years

  2. 17 years

  3. 16 years

  4. 20 years

  5. 19 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Present average age of the family of 9 members is 26 years.

So, present sum of the ages of all the 9 members = 26 * 9 = 234 years

Now, sum of the ages at the time of birth of the youngest member = 234 - (8 * 10 + 10)

= 144 years

So, average age of 8 members at the time of birth of the youngest member = 144/8 = 18 years

Multiple choice

The ratio between the present ages of P and Q is 3 : 7. If after 5 years, the age of Q becomes twice the age of P, then find the present age of P.

  1. 15 years

  2. 12 years

  3. 21 years

  4. 18 years

  5. 24 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the present age of P be 3x years.

So the present age of Q be 7x years.

Now, after 5 years, P's age = 3x + 5 years and Q's age = 7x + 5 years

So, according to question,

2(3x + 5) = 7x + 5

On solving this equation, we get

x = 5

So, the present age of P is 3x = 3 * 5 = 15 years.

Multiple choice

Ten years ago, Rekha's age was 10 years more than twice of Megha's age. Six years hence, sum of their ages will be 78 years. Find the ratio of their present ages.

  1. 21 : 12

  2. 2 : 1

  3. 1 : 2

  4. 31 : 35

  5. 25 : 41
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Ten years ago, let Megha's age be x years. 

Then, Rekha's age = 2x + 10 years 

So, present age of Rekha = 2x + 10 + 10 = 2x + 20 years and present age of Megha = x + 10 years 

Now, six years hence, Rekha's age = 2x + 20 + 6 = 2x + 26 years and Megha's age = x + 10 + 6 = x + 16 years 

According to question,

2x + 26 + x + 16 = 78

x = 12

So, ten years ago, Megha's age = 12 years and Rekha's age = 2 x 12 + 10 = 34 years 

Now, present age of Rekha = 34 + 10 = 44 years and pressent age of Megha = 12 + 10 = 22 years

So, ratio of their present ages = 44 : 22 = 2 : 1

Multiple choice

Akash is 30 years younger than his father. Four years ago, Akash was 2/5th as old as his father. How old will Akash's father be 6 years from today?

  1. 50 years

  2. 54 years

  3. 40 years

  4. 60 years

  5. 64 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the present age of father be x years.

Then, present age of Akash = x - 30 years 

Four years ago, Akash's father's age = x - 4 years and Akash's age = x - 30 - 4 = x - 34 years

According to the question,

x - 34 = 2/5(x - 4)

x = 54

Akash's father's present age = 54 years 

So, father's age after 6 years = 54 + 6 = 60 years

Multiple choice

The ages of A and B are in the ratio 4 : 5. After 14 years, the ratio of their ages will be 6 : 7. What was the difference of their ages 5 years ago?

  1. 5 years

  2. 7 years

  3. 6 years

  4. 4 years

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

Let the present age A be 4x years and that of B be 5x years. 

After 14 years, A's age = 4x + 14 years and B's age = 5x + 14 years

Now, according to question, 

(4x + 14)/(5x + 14) = 6/7

x = 7

Now, present age of A = 4 * 7 = 28 years and present age of B = 5 * 7 = 35 years

Age of A 5 years ago = 28 - 5 = 23 and B's age 5 years ago = 35 - 5 = 30 years

So, the difference of ages of A and B is 30 - 23 = 7 years.

Multiple choice

A father is 14 times older than his son. After 12 years, his age will be 20/7 of the age of his son. Find the present age of the father.

  1. 30 years

  2. 32 years

  3. 26 years

  4. 28 years

  5. 24 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 father = 14x years

After 12 years, son's age = x + 12 years and father's age = 14x + 12 years 

Now, according to question,

20/7(x + 12) = 14x + 12

x = 2

So, present age of father = 14x = 14 * 2 = 28 years

Multiple choice

The sum of the present ages of both father and son is 86 years. Five years ago, the father was 2 years less than twice as old as his son at that time. Find the present age of the son.

  1. 31 years

  2. 30 years

  3. 32 years

  4. 34 years

  5. 36 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the present age of father be x years and that of the son 86 - x years.

Five years ago, father's age = x - 5 years and son's age = (86 - x - 5) = 81 - x years

Now, according to question,

x - 5 = 2(81 - x) - 2

x = 55

So, present age of father = 55 years 

Therefore, present age of son = 86 - 55 = 31 years

Multiple choice

If a son is younger than his father by 23 years and 5 years ago, the father was 30 years old, then what is the sum of their ages after 10 years?

  1. 70 years

  2. 80 years

  3. 72 years

  4. 67 years

  5. 52 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the present age of father be x years.

Five years ago, father's age = x - 5 years

Now, according to question,

x - 5 = 30

x = 35 years

So, father's present age = 35 years

So, son's present age = 35 - 23 = 12 years 

Now, total age of father and son after 10 years = (35 + 10) + (12 + 10) = 67 years

Multiple choice

The age of father is 2 years more than twice his son's present age. After 7 years, the sum of their ages will be 121 years. Find the present age of the father.

  1. 70 years

  2. 76 years

  3. 72 years

  4. 60 years

  5. 66 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the present age of the son be x years.

Then, present age of father = 2x + 2 years 

Now, after 7 years, son's age = x + 7 years and father's age = 2x + 2 + 7 = 2x + 9 years

Now, according to question, 

x + 7 + 2x + 9 = 121 

x = 35

So, present age of son = 35 years

Therefore, present age of father = 35 * 2 + 2 = 72 years

Multiple choice

Anuj is 2 years younger than Rakesh and Rakesh is 39 years younger than Rahul. If the age of Rahul is 3 times of the sum of ages of Anuj and Rakesh, then find the present age of Rahul.

  1. 48 years

  2. 46 years

  3. 40 years

  4. 50 years

  5. 44 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the present age of Rahul be x years.

Then, present age of Rakesh = x - 39 years 

So, present age of Anuj = x - 39 - 2 = x - 41 

Now, according to question,

x = 3(x - 39 + x - 41)

x = 48 years