Quantitative Aptitude

Problems on Ages

1,744 Questions
All Translate multiples, fractions, and percentages 518 Use two ratios from different dates 500 Convert an age ratio into actual ages 258 Handle averages and changing groups 167 Generational age chains 111 Recognize equal age gaps 101 Product of ages 68 Ages in arithmetic progression 11 Division of lifespan 9

Problems on Ages Questions

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

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

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.

Multiple choice

The sum of the present ages of A and B is 11 times the difference of their ages. Six years hence, the total of their ages will be 15 times the difference of their ages. What is the present age of the older person?

  1. 25 years

  2. 20 years

  3. 15 years

  4. 18 years

  5. 16 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the present age of A be x years and that of B be y years. According to question, x + y = 11(x - y) -5x + 6y = 0 --------------------(1) Six years hence, age of A = x + 6 and that of B = y + 6 years Again, according to question, (x + 6) + (y + 6) = 15[(x + 6) - (y + 6)]

  • 7x + 8y = -6 --------------------(2) On solving equations (1) and (2), we get x = 18 and y = 15 So, the age of the older person is 18 years. Correct Answer: 18 years
Multiple choice

Five years ago, a grandfather was 7.5 times older than his grandson. After 15 years from today, the grandfather will be 20/7 times as old as his grandson will be at that time. What was the ratio of the ages of grandfather and grandson 1 year ago?

  1. 16 : 3

  2. 16 : 5

  3. 15 : 2

  4. 12 : 5

  5. 16 : 7
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let 5 years ago, grandson's age be x years and grandfather's age be 7.5x years. Now, after 15 years, grandson's age = x + 5 + 15 = x + 20 years and grandfather's age = 7.5x + 5 + 15 = 7.5x + 20 years Now, according to question, 20(x + 20)/7 = 7.5x + 20 x = 8 So, the present age of grandson = 8 + 5 = 13 years and that of the grandfather = 7.5 x 8 + 5 = 65 years One year ago, grandfather's age = 65 - 1 = 64 years and grandson's age = 13 - 1 = 12 years Now, ratio of their ages 1 year ago = 64 : 12 = 16 : 3

Multiple choice

A's present age is thrice his son's present age and 6/11th of his father's present age. The average present age of all of them is 38 years. What is difference between the present ages of A's father and A's son?

  1. 54 years

  2. 68 years

  3. 64 years

  4. 70 years

  5. 60 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the present age of A be x years. So, present age of the son = x/3 years and A's father's age = 11x/6 years Now, according to question, (x + x/3 + 11x/6)/3 = 38 19x/18 = 38 x = 36 So, present age of A = 36 years Therefore, present age of A's son = 36/3 = 12 years and that of A's father = 11 x 36/6 = 66 years Now, difference between A's father age and A's son age = 66 - 12 = 54 years

Multiple choice

A father has two sons - Amit and Anil. Amit's age is 1/2 of his father's age. The father's age will be 5/3 of Anil's age after 4 years. If the sum of the present ages of Amit and Anil is 27 years, then what is Amit's present age?

  1. 14 years

  2. 13 years

  3. 16 years

  4. 15 years

  5. 18 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the present age of Amit be x years and that of Anil be y years.

So, present age of father = 2x years

Now, sum of the ages of Amit and Anil is 27 years.

So, x + y = 27  -------------------(1)

After 4 years, father's age = 2x + 4 and Anil's age = y + 4

According to question,

2x + 4 =5/3(y + 4)

6x - 5y = 8 ------------------------(2)

After solving equations (1) and (2), we get

x = 13 and y = 14

So, the present age of Amit is 13 years.

Multiple choice

In a family, the ratio of the present ages of son, mother, father and grandfather is 1 : 4 : 5 : 11. The average age of son, mother and father is 20 years. What is the age of grandfather?

  1. 88 years

  2. 77 years

  3. 55 years

  4. 66 years

  5. 99 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the present age of son be 1x years, that of mother be 4x years, that of father be 5x years and that of grandfather be 11x years. According to question, (1x + 4x + 5x)/3 = 20 x = 6 So, present age of grandfather = 11 x 6 = 66 years

Multiple choice

Vivek is 3 times as old as Tarun. Sourabh was twice as old as Vivek 4 years ago. In 4 years, Vivek will be of 31 years. What is the present age of Tarun and Sourabh, respectively?

  1. 9 and 50

  2. 9 and 54

  3. 12 and 60

  4. 9 and 46

  5. 50 and 9
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

It is a correct answer .Solution-Let Vivek's present age = x Similarly,Let Tarun's present age = y and Sourabh's present age = z
We know, x = 3*y z-4 = 2*(x-4) and (x+4) = 31 (Given In statement) x=27 Therefore, y = 9 z = 50 The age of tarun is 9 years and of sourabh is 50 years.