# Age problems with solution

**Question1**: A boy said to his friends, "When I was born, my father was as old as I am now". If his father's age will be 60 after 6 years, find the son's present age.

Option 1 : 25

Option 2 : 33

Option 3 : 27

Option 4 : 30

Answer : C

**Explanation**: Father's present age

= 60-6

= 54

Let the son's present age be x years.

The father was x years old when the son was born(before x years).

54-x = x

x = 27

**Question2**: A father's age is two and a half times more than his son's age. 5 years ago, he was six times the age of his son. Find the father's present age.

Option 1 : 35

Option 2 : 40

Option 3 : 38

Option 4 : 31

Answer : A

**Explanation**: Let the son's present age be x years.

Father's age

= x+2.5x

= 3.5x

(3.5x-5) = 6(x-5)

3.5x-5=6x-30

2.5x=25

x=10

Father's present age = 35

**Question3**: The ratio of the ages of a mother and a daughter are in the ratio 3:1. The product of their ages is 363. Find the daughter's age after 4 years.

Option 1 : 11

Option 2 : 14

Option 3 : 15

Option 4 : 10

Answer : C

**Explanation**: Mother's present age = 3x

Daughter's present age = x

3x*x = 363

3x² = 363

x² = 121

x = 11

Daughter's age after 4 years = 15

**Question4**: The present ages of three people in a family are in the ratio 3:5:7. If the sum of their ages before 5 years was 60, find the age of the youngest.

Option 1 : 12

Option 2 : 18

Option 3 : 6

Option 4 : 15

Answer : D

**Explanation**: Let their present ages be 3x,5x and 7x.

Sum of their ages before 5 years

= 3x-5+5x-5+7x-5

= 15x-15 = 60

Solving,

x=5

Age of the youngest

= 3x = 15

**Question5**: The difference between the ages of A and C is half the age of B. The difference between the ages of A and B is one-sixth of the age of C. If the sum of the ages of B and C is 32, find the age of A.

Option 1 : 25

Option 2 : 22

Option 3 : 20

Option 4 : 27

Answer : B

**Explanation**: A-C=B/2

A-B=C/6

B+C=32

Solving the three equations,

A=22

**Question6**: The average age of two brothers in a family is 21. The average drops to 19 when the age of the third brother is also included. Find the age of the third brother.

Option 1 : 18

Option 2 : 19

Option 3 : 15

Option 4 : 21

Answer : C

**Explanation**: Let the ages of the three brothers be x,y and z.

(x+y)/2 = 21

x+y=42

(x+y+z)/3=19

x+y+z=57

42+z=57

z=15

**Question7**: 5 years ago, 1/5th of Keith's age was equal to 1/7th of Dora's age. The average of their present ages is 29. Find Keith's age after 5 years.

Option 1 : 30

Option 2 : 38

Option 3 : 35

Option 4 : 25

Answer : A

**Explanation**: (K-5)/5 = (D-5)/7

(K+D)/2 = 29

Solving, K=25, D=33

K+5=30

**Question8**: Anju is three years older than Sanju who is five years older than Manju. The sum of their ages is 73. Find the age of Sanju.

Option 1 : 20

Option 2 : 25

Option 3 : 28

Option 4 : 30

Answer : B

**Explanation**: A=S+3

S=M+5

A+S+M=73

S+3+S+S-5=73

S=25

**Question9**: The present ages of Ram and Raj differ by 7. Five years back, Raj was twice the age of Ram. Find the age of Ram after 4 years.

Option 1 : 16

Option 2 : 20

Option 3 : 21

Option 4 : 25

Answer : A

**Explanation**: Let Raj’s age be x and Ram’s age be y.

x-y=7

x-5=2(y-5)

Solving the two linear equations,

y=12, y+4=16

**Question10**: The ages of Vikas and Nikash are in the ratio of 5:3. If Vikas is 8 years elder than Nikash, find the age of Nikash.

Option 1 : 10

Option 2 : 12

Option 3 : 15

Option 4 : 20

Answer : B

**Explanation**: V=8+N

(V/N)=(5/3)

Solving the two equations,

N =12

**Question11**: Today is Anish's birthday. One year from today, he will be twice as old as he was 10 years ago. How old is Anish today?

Option 1 : 21 years

Option 2 : 23 years

Option 3 : 22 years

Option 4 : 25 years

Answer : A

**Explanation**: Let his present age be x.

x+1 = 2(x-10)

Solving, x = 21

**Question12**: At present, Shyam is twice as old as his sister. Three years back, he was thrice her age. Find his sister's present age.

Option 1 : 8

Option 2 : 9

Option 3 : 12

Option 4 : 6

Answer : D

**Explanation**: Let his sister's present age be x.

Shyam's present age = 2x

2x-3 = 3(x-3)

x = 6

**Question13**: In a group of 4 friends, P is the eldest and R is the youngest. Neither is of the same age as the others. The sum of the ages of R and S is greater than twice the age of Q. Who is the second eldest?

Option 1 : P

Option 2 : Q

Option 3 : R

Option 4 : S

Answer : C

**Explanation**: R+S>2Q

Q<R+S/2

Since R<Q, S>Q

R<Q<S<P

**Question14**: On a man's tombstone, it is said that one sixth of his life was spent in childhood and one twelfth as a teenager. One seventh of his life passed between the time he became an adult and the time he married; five years later, his son was born. Alas, the son died four years before he did. He lived to be twice as old as his son did. How old did the man live to be?

Option 1 : 42 years

Option 2 : 48 years

Option 3 : 70 years

Option 4 : 84 years

Answer : D

**Explanation**: Let the man’s age be x years and his son’s age be y years.

(x/6)+(x/12)+(x/7)+5+y+4=x

x=2y

Solving, x=84

**Question15**: A father is three times as old as his son. After fifteen years the father will be twice as old as his son's age at that time. Hence the father's present age is

Option 1 : 36

Option 2 : 42

Option 3 : 45

Option 4 : 48

Answer : C

**Explanation**: F=3S

F+15=2(S+15)

Solving the two equations, F=45

**Question16**: A wizard named Nepo says "I am only three times my son's age. My father is 40 years more than twice my age. Together the three of us are a mere 1240 years old." How old is Nepo?

Option 1 : 360

Option 2 : 240

Option 3 : 120

Option 4 : 480

Answer : A

**Explanation**: N=3S

F=2N+40

F+N+S=1240

Solving these, N=360

**Question17**: A man has three daughters. The present ages of all three of them are square numbers. The sum of their ages after 5 years is 41. Find the age of his eldest daughter after 2 years.

Option 1 : 18

Option 2 : 16

Option 3 : 11

Option 4 : 9

Answer : A

**Explanation**: x,y and z are square numbers.

(x+5)+(y+5)+(z+5)=41

x+y+z=26

By trial and error method, their ages are 1, 9 and 16.

The age of his eldest daughter after 2 years is 18.

**Question18**: Thirteen years back, my mother was thrice my age and two years back, she was twice my age. Find my mother’s present age.

Option 1 : 58

Option 2 : 46

Option 3 : 28

Option 4 : 24

Answer : B

**Explanation**: Let my age be x and my mother’s age be y.

y-13 = 3(x-13)

y-2 = 2(x-2)

Solving the two equations, y=46

**Question19**: Ram and Raj are twins. The sum of their ages combined with their father’s age is 47. Their father’s age at the time of their birth was 29. Find the age of Ram.

Option 1 : 6

Option 2 : 9

Option 3 : 11

Option 4 : 14

Answer : A

**Explanation**: R+R+F=47

F-R=29

Solving the two equations, R=6

**Question20**: The ages of Pooja and Deepa are in the ratio 4:5. 4 years ago, their ages were in the ratio 8:11. Find Pooja's present age.

Option 1 : 12

Option 2 : 15

Option 3 : 14

Option 4 : 9

Answer : A

**Explanation**: Pooja's present age=4x

Deepa's present age=5x

(4x-4):(5x-4) = 8:11

44x-44=40x-32

4x=12

x=3

4x=12

**Question21**: A boy is 8 years older than his sister. Two years ago, he was twice his sister's age. Find his present age.

Option 1 : 20

Option 2 : 10

Option 3 : 18

Option 4 : 16

Answer : C

**Explanation**: B=8+S

(B-2)=2(S-2)

B-2=2S-4

8+S-2=2S-4

S=10

B=18

**Question 22**: The sum of the ages of Lily and Nancy is twice the difference of their ages. Find the ratio of Nancy's age to Lily's age.

Option 1 : 1:3

Option 2 : 3:1

Option 3 : 1:2

Option 4 : 2:1

Answer : A

**Explanation**: L+N=2(L-N)

L+N=2L-2N

3N=L

N/L = 1/3

N:L=1:3

**Question23**: Five years ago, the sum of my age and my mother's age was equal to my father's age. If my father is 6 years elder than my mother, find my present age.

Option 1 : 12

Option 2 : 11

Option 3 : 10

Option 4 : 6

Answer : B

**Explanation**: Let my present age be X.

(X-5)+(M-5)=(F-5)

X+M=F+5

X=F-M+5

F-M=6

X=6+5=11

**Question24**: Flora is twice Tara's age. After 10 years, Tara will be two-third of Flora's age. Find Flora's present age.

Option 1 : 10

Option 2 : 15

Option 3 : 18

Option 4 : 20

Answer : D

**Explanation**: F=2T

(T+10)=(2/3)*(F+10)

3T+30=2F+20

2F-3T=10

2*(2T)-3T=10

T=10

F=2T=20

**Question25**: Nina is 9 years older than Angel. Two years ago, Angel's age was half that of Nina's. Find Angel's present age.

Option 1 : 10

Option 2 : 11

Option 3 : 15

Option 4 : 18

Answer : B

**Explanation**: N=A+9

(A-2)=(1/2)*(N-2)

2A-4=N-2

2A-4 = A+9-2

A = 11

**Question26**: The total age of X and Y is 10 years more than the total age of Y and Z. Find the difference between the ages of X and Z.

Option 1 : 5

Option 2 : 10

Option 3 : 15

Option 4 : 20

Answer : B

**Explanation**: X+Y = 10+(Y+Z)

X-Z=10

**Question27**: The present ages of A,B and C are in the ratio 3:5:8. Eight years ago, the sum of their ages was 40. Find B's present age.

Option 1 : 12

Option 2 : 20

Option 3 : 24

Option 4 : 40

Answer : B

**Explanation**: Let the present ages of A, B and C be 3x, 5x and 8x respectively.

(3x-8)+(5x-8)+(8x-8)

= 40

16x-24=40

2x-3=5

x=8/2 = 4

B's present age=5x=20

**Question 28**: My brother is 5 years elder to me. My father was 30 years of age when my sister was born while my mother was 32 years of age when I was born. If my sister was 5 years of age when my brother was born, then what was the age my father when my brother was born?

Option 1 : 32

Option 2 : 35

Option 3 : 37

Option 4 : 40

Answer : B

**Explanation**: Let my present age be x.

Brother's age = x+5

My sister is five years elder than my brother.

Sister's age = x+10

My father was 30 years of age when my sister was born.

Father's age

= x+10+30

= x+40

My mother was 32 years of age when I was born.

Mother's age

= x+32

Father's age when my brother was born

= x+40-(x+5)

= 35

**Question29**: Ajay's father was 32 years of age when he was born while his mother was 29 years old when his sister three years younger to him was born. What is the difference between the ages of his parents?

Option 1 : 6

Option 2 : 7

Option 3 : 5

Option 4 : 4

Answer : A

**Explanation**: Let Ajay's age be x.

His father's age

= x+32

His sister's age

= x-3

His mother's age

= x-3+29

= x+26

Difference between the ages of his parents

= (x+32)-(x+26)

= 6

**Question30**: The ages of two person P and Q differ by 14 years. 6 years ago, P was thrice as old as Q. Find the present age of Q.

Option 1 : 13

Option 2 : 15

Option 3 : 16

Option 4 : 18

Answer : D

**Explanation**: P-Q = 14 -----(I)

(P-6) = 3(Q-6)

P-3Q = -12 -----(II)

Solving (I) and (II),

Q = 13

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