Problems on Ages Practice Test for Aptitude Exams -- Free Practice

Question 1

The age of a person is 8 years more than thrice the sum of the ages of his two grandsons who were twins. After 8 years, his age will be 10 years more than twice the sum of the ages of his grandsons. Then the age of the person when the twins were born is:

A

86 years✓✗

B

73 years✓✗

C

68 years✓✗

D

63 years✓✗

Explanation

Let the person's current age = P, and each twin's current age = G (combined = 2G).
P = 8 + 3(2G) = 8 + 6G
After 8 years: P + 8 = 10 + 2(2G + 16) = 42 + 4G, so P = 34 + 4G
Equating: 8 + 6G = 34 + 4G ⇒ 2G = 26 ⇒ G = 13
P = 8 + 6(13) = 86
Age when twins were born = P - G = 86 - 13 = 73

Question 2

The ages of two persons are in the ratio 5:7. Eighteen years ago their ages were in the ratio of 8:13. Their present ages (in years) are:

A

50, 70✓✗

B

70, 50✓✗

C

40, 56✓✗

D

None of these✓✗

Explanation

Let the present ages be 5x and 7x.
18 years ago: 13(5x - 18) = 8(7x - 18)
65x - 234 = 56x - 144
9x = 90, so x = 10
Present ages = 5x = 50 and 7x = 70

Question 3

The combined age of husband and wife on their 20th wedding anniversary was twice than it was at the time of wedding. If the husband is 3 years older than his wife. How old was he at the time of his marriage?

A

29 years✓✗

B

38.5 years✓✗

C

21.5 years✓✗

D

32 years✓✗

Explanation

Let the ages at the time of marriage be H (husband) and W (wife), with H = W + 3. After 20 years the combined age is H + W + 40 = 2(H + W), so H + W = 40.
With H - W = 3: H = 432 = 21.5 years.

Question 4

Neha's mother was four times her age 12 years ago. She will be twice as old as Neha 12 years from now. What is the present age of Neha's mother ?

A

49 years✓✗

B

57 years✓✗

C

60 years✓✗

D

65 years✓✗

Explanation

Let Neha's present age be n and her mother's age m. Twelve years ago: m - 12 = 4(n - 12). Twelve years from now: m + 12 = 2(n + 12).
From the first, m = 4n - 36. From the second, m = 2n + 12.
So 4n - 36 = 2n + 12, giving n = 24 and m = 2 × 24 + 12 = 60 years.

Question 5

The ratio between the present ages of A and B is 3:5 respectively. If the difference between B's present age and A's age after 4 years is 2 , what is the total of A's and B's present ages?

A

24 years✓✗

B

32 year✓✗

C

48 years✓✗

D

cannot be determined✓✗

Explanation

Let the present ages be 3x and 5x. A's age after 4 years = 3x + 4, so 5x - (3x + 4) = 2, which gives x = 3.
A = 9 and B = 15, so the total = 9 + 15 = 24 years.

Question 6

The ratio of the present age of father to that of son is 7:2. After 10 years their ages will be in the ratio of 9:4. The present ages of the father is

A

35 years✓✗

B

40 years✓✗

C

30 years✓✗

D

25 years✓✗

Explanation

Let the present ages be 7x and 2x. 7x + 102x + 10 = 94.
28x + 40 = 18x + 90, so x = 5.
The father's present age = 7 × 5 = 35 years.

Question 7

If the ratio of present ages of Jeet and Jay is 5:7 and after 6 years the ratio will be 3:4, what is the present age of Jay?

A

42✓✗

B

30✓✗

C

36✓✗

D

None of these✓✗

Explanation

Let the present ages of Jeet and Jay be 5x and 7x.
5x + 67x + 6 = 34, so 20x + 24 = 21x + 18 and x = 6.
Jay's present age = 7 × 6 = 42 years.

Question 8

Rohan's age is five times Ajay’s and seven-eighteenth of Meena’s age. The sum of the ages of all three of them is 132 years. How much younger is Ajay to Meena?

A

56 years✓✗

B

83 years✓✗

C

27 years✓✗

D

Cannot be determined✓✗

Explanation

Let Ajay's age be a. Rohan's age = 5a and Rohan's age = 718 of Meena's, so Meena's age = 187 × 5a = 90a7.
a + 5a + 90a7 = 132, so 132a7 = 132 and a = 7.
Ajay = 7, Rohan = 35 and Meena = 90. Ajay is younger than Meena by 90 - 7 = 83 years.

Question 9

The average age of 10 students and their teacher is 15 years. The average age of the first seven students is 15 yr and that of the last three is 11 yr. What is the teacher's age?

A

33 years✓✗

B

30 years✓✗

C

27 years✓✗

D

24 years✓✗

Explanation

The total age of the 10 students and the teacher = 11 × 15 = 165.
The total age of the students = 7 × 15 + 3 × 11 = 105 + 33 = 138.
The teacher's age = 165 - 138 = 27 years.

Question 10

The present ages of Aman and Nina are 59 and 37 years, respectively. What was the ratio of the ages of Nina and Aman 13 years ago?

A

3:2✓✗

B

46:25✓✗

C

12:23✓✗

D

8:3✓✗

Explanation

Thirteen years ago Nina was 37 - 13 = 24 and Aman was 59 - 13 = 46.
The ratio = 24 : 46 = 12 : 23.

Question 11

12 years ago, age of P was 3 times the age of Q. After 12 years, ratio of ages of Q to P will be 2:3. What is the present age of P?

A

54 years✓✗

B

36 years✓✗

C

24 years✓✗

D

144 years✓✗

Explanation

Let the present ages of P and Q be p and q. 12 years ago: p - 12 = 3(q - 12), so p = 3q - 24.
After 12 years: q + 12p + 12 = 23, so 3q + 36 = 2p + 24 = 6q - 48 + 24.
3q + 36 = 6q - 24, so q = 20 and p = 36.
P's present age is 36 years.

Question 12

The present ages of A and B are 42 and 36 years, respectively. After K years, the ratio of ages of B to A will be 15:17.What is value of K?

A

9 years✓✗

B

12 years✓✗

C

5 years✓✗

D

3 years✓✗

Explanation

36 + K42 + K = 1517, so 17(36 + K) = 15(42 + K).
612 + 17K = 630 + 15K, so 2K = 18 and K = 9 years.

Question 13

A father is 4 times as old as his son. 8 years hence, the ratio of father’s age to the son’s age will be 20:7. What is the sum of their present ages?

A

50✓✗

B

72✓✗

C

68✓✗

D

65✓✗

Explanation

Let the son's present age be s and the father's = 4s.
After 8 years: 4s + 8s + 8 = 207, so 28s + 56 = 20s + 160 and s = 13.
The father is 52. The sum of their present ages = 13 + 52 = 65.

Question 14

At present, the ratio between the ages of Amit and Dhiraj is 5 : 4. After 6 years, Amit’s age will be 26 years. What is the age of Dhiraj at present?

A

12 years✓✗

B

16 years✓✗

C

19 ½ years✓✗

D

21 years✓✗

Explanation

After 6 years Amit will be 26, so he is 20 now.
Amit : Dhiraj = 5 : 4, so Dhiraj's present age = 45 × 20 = 16 years.

Question 15

Find Nikhil's present age, if

I. Five years ago, Nikhil's age was double that of his daughter's age at that time.
II. Present ages of Nikhil and his daughter are in the ratio of 11:6 respectively
III. Five years hence, the respective ratio of Nikhil's age and his daughter age will become 12:7

A

Only I and II✓✗

B

Only II and III✓✗

C

Only I and III✓✗

D

Any two of the three✓✗

Explanation

Any two of the three statements are enough. With I and II: N - 5 = 2(D - 5) and N : D = 11 : 6 gives 11k - 5 = 12k - 10, so k = 5 and N = 55. With II and III: 11k + 56k + 5 = 127 gives 77k + 35 = 72k + 60, so k = 5 and N = 55. With I and III the same value N = 55 is found.
So any two of the three statements give Nikhil's age.

Question 16

The average age of 19 boys and the class teacher is 16 years. If the ages of the class teacher and one of the boys are excluded, the average age reduces to 15 years. What is the age of the class teacher ?

A

40 years✓✗

B

36 years✓✗

C

31 years✓✗

D

Data Inadequate✓✗

Explanation

The total age of 19 boys and the teacher = 20 × 16 = 320.
After excluding the teacher and one boy, the 18 boys have a total = 18 × 15 = 270.
The teacher's age + the excluded boy's age = 50, but the age of the teacher alone cannot be found without the boy's age.
The data is inadequate.

Question 17

15 years ago, a father was three times as old as his daughter. Now the father is only twice as old as his daughter. Find the sum of the present ages of daughter and father.

A

54✓✗

B

65✓✗

C

90✓✗

D

108✓✗

Explanation

Let the daughter's present age be d, so the father's present age = 2d.
15 years ago: 2d - 15 = 3(d - 15), so 2d - 15 = 3d - 45 and d = 30.
The father is 60. The sum of the present ages = 30 + 60 = 90.

Question 18

The sum of the ages of 4 children born at the intervals of the 3 years each is 58 years. What is the age of the youngest child?

A

4 years✓✗

B

6 years✓✗

C

8 years✓✗

D

10 years✓✗

Explanation

Let the age of the youngest child be a. The ages are a, a + 3, a + 6 and a + 9.
Sum = 4a + 18 = 58, so a = 10 years.

Question 19

Rohan was 4 times as old as his son 6 years ago. After 6 years Rohan will be twice as old as his son. What is son's present age?

A

10 years✓✗

B

12 years✓✗

C

14 years✓✗

D

18 years✓✗

Explanation

Let Rohan's age be R and his son's age be S. Six years ago: R - 6 = 4(S - 6), so R = 4S - 18.
After 6 years: R + 6 = 2(S + 6), so R = 2S + 6.
4S - 18 = 2S + 6, so S = 12.
The son's present age is 12 years.

Question 20

My father was 30 years of age when my sister was born. My mother was 38 years of age when I was born. My sister was 6 years of age when my brother was born who is 3 years elder to me. What was the age of my father and mother during the birth of my brother?

A

41, 36✓✗

B

24, 28✓✗

C

28, 24✓✗

D

36, 35✓✗

Explanation

The father was 30 when the sister was born. The brother was born when the sister was 6, so the father's age at the brother's birth = 30 + 6 = 36.
The mother was 38 when I was born. The brother is 3 years older than me, so at his birth she was 38 - 3 = 35.
The ages are 36 and 35.

Question 21

The difference between the ages of two brothers is 8 years. If 12 years ago, the elder one was twice as old as his younger brother, what is the present age of the younger brother?

A

20✓✗

B

28✓✗

C

24✓✗

D

26✓✗

Explanation

Let the younger brother's present age be y, so the elder's age = y + 8.
12 years ago: y + 8 - 12 = 2(y - 12), so y - 4 = 2y - 24 and y = 20.
The younger brother is 20 years old.

Question 22

The ratio of the current ages of Ajay and Vijay is 7:4. The ratio between Ajay’s age 6 years ago and Vijay’s age 6 years from now is 1:1. Find the ratio between Ajay’s
age 12 years hence and Vijay’s age 12 years ago.

A

12:1✓✗

B

10:1✓✗

C

1:1✓✗

D

None of these✓✗

Explanation

Let the ages of Ajay and Vijay be 7x and 4x. Six years ago Ajay's age = 7x - 6 and 6 years from now Vijay's age = 4x + 6.
7x - 6 = 4x + 6, so x = 4. Ajay is 28 and Vijay is 16.
Ajay's age after 12 years = 40 and Vijay's age 12 years ago = 4.
The ratio = 40 : 4 = 10 : 1.

Question 23

If the ratio of the ages of Shweta and Veena was 5:6 six years ago and it will become 10:11 in 4 years from now, then find the present age of Veena.

A

16✓✗

B

18✓✗

C

10✓✗

D

12✓✗

Explanation

Let the present ages of Shweta and Veena be S and V. Six years ago: S - 6V - 6 = 56, so 6S = 5V + 6.
After 4 years: S + 4V + 4 = 1011, so 11S = 10V - 4.
From the first, S = 5V + 66. Then 11(5V + 6) = 6(10V - 4), so 55V + 66 = 60V - 24 and V = 18.

Question 24

Total age of P and Q is 15 years more than the total age of Q and R. By how many years is R younger than P?

A

15 years✓✗

B

30 years✓✗

C

Data insufficient✓✗

D

None of these✓✗

Explanation

P + Q = Q + R + 15, so P - R = 15.
R is younger than P by 15 years.

Question 25

X is twice as old as Y was when X was as old as Y is. The sum of their ages is 49 years. The difference between their ages is...

A

23 Years✓✗

B

21 Years✓✗

C

14 Years✓✗

D

7 Years✓✗

Explanation

Let X's age now be x and Y's age now be y. X was as old as y was (x - y) years ago, and Y's age then = y - (x - y) = 2y - x.
X is twice that age, so x = 2(2y - x), which gives 3x = 4y, so x : y = 4 : 3.
The sum = 7 parts = 49, so 1 part = 7.
The difference between their ages = 1 part = 7 years.