Important Formulas / Properties:
Consider x, as the age of an individual
 If the current age of the person is x, then n times the age is nx
 If the current age of the person is y, then age n years ago = y – n
 If the current age of the person is z, then age n years later = z + n
 The age of the person in a ratio a: b will be ax and bx
 If the current age of the person is s , then 1/n of the age is s/n
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Question 1

Sachin was twice as old as ajay, 10 years back. How old is ajay today, if sachin will be 40 years old, 10 years hence?
A

18

B

25

C

15

D

20

Question 1 Explanation:
S+10 = 40
S = 30
S  10 = 2(A  10)
A = 20
S = 30
S  10 = 2(A  10)
A = 20
Question 2

One year ago, a mother was four times as old as ger daughter. Six years hence, the age of the mother will exceed twice the age of her daughter by 9 years. The ratio of the present ages of the mother and her daughter is?
A

9:2

B

12:5

C

11:3

D

13:4

Question 2 Explanation:
M  1 = 4(D  1)
4D  M = 3
M + 6 = 2(D+6)+9
M  2D = 15
Solving,
2D = 18
D = 9
M = 33
M : D = 11 : 3
4D  M = 3
M + 6 = 2(D+6)+9
M  2D = 15
Solving,
2D = 18
D = 9
M = 33
M : D = 11 : 3
Question 3

Ratio of jehin’s age to nitin’s age is equal to 4:3, jehin will be 26 years old after 6 years. How old is nitin now?
A

12 yrs

B

15 yrs

C

19 yrs

D

21 yrs

Question 3 Explanation:
J = 26  6 = 20
J  N = 4 : 3
N = 15
J  N = 4 : 3
N = 15
Question 4

The sum of the ages of A and B is 45 years. Five years ago, the poduct of their ages was four times the age of A at that time. The present ages of A and B, Respectively are?
A

25 years

B

39 years

C

36 years

D

None of these

Question 4 Explanation:
A+B=45
(A5)(B5) = 4(A5)
B  5 = 4
B = 9
A = 36
(A5)(B5) = 4(A5)
B  5 = 4
B = 9
A = 36
Question 5

Jayant is as much younger to akil as he is older to pranav. If the sum of the age of akil and pranav is 48 years, what is the age of jayant?
A

20

B

24

C

30

D

None of these

Question 5 Explanation:
A  J = J  P
2J = A + P
A + P = 48
2J = 48
J = 24
2J = A + P
A + P = 48
2J = 48
J = 24
Question 6

Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, Find the difference between the agres of R and Q?
A

1 year

B

2 year

C

25 year

D

Data Inadequate

Question 6 Explanation:
R  Q = Q  T
(R+T) = 2Q
Now given that, (R+T) = 50
2Q = 50
Q = 25
Without knowing the value of R or T, we cant find R Q. Hence, Data inadequate
(R+T) = 2Q
Now given that, (R+T) = 50
2Q = 50
Q = 25
Without knowing the value of R or T, we cant find R Q. Hence, Data inadequate
Question 7

The ratio of the age of pramond and the age of akash is 3:5 and sum of their ages is 80 years. The ratio of their ages after 10 years will be?
A

2:3

B

1:2

C

3:2

D

3:5

Question 7 Explanation:
Let the ages of pramod and akash be 3x and 5x
3x + 5x = 80
8x = 80 ,x = 10
3x=30
5x=50
Ratio of theie age after 10 years = (3x+10) : (5x+10)
=> 40 : 60 = 2 : 3
3x + 5x = 80
8x = 80 ,x = 10
3x=30
5x=50
Ratio of theie age after 10 years = (3x+10) : (5x+10)
=> 40 : 60 = 2 : 3
Question 8

The ratio of the ages of mmen and neena is 4:3. The sum of their ags is 28 years. The ratio of their ages after 8 years will be?
A

4:3

B

12:11

C

7:4

D

6:5

Question 8 Explanation:
Let the ages of meena and neena be 4x and 3x respectively
M : N = 4 : 3
M + N = 28
4x + 3x = 28
X= 4
M= 16
N=12
(M+8) : (N+8) = 24 : 20 = 6 : 5
M : N = 4 : 3
M + N = 28
4x + 3x = 28
X= 4
M= 16
N=12
(M+8) : (N+8) = 24 : 20 = 6 : 5
Question 9

Shankar is younger than Raju by 7 years. If their ages are in the respective rtio of 7:9, how old is Shankar?
A

16yrs

B

18 yrs

C

28 yrs

D

24.5 yrs

Question 9 Explanation:
S = R  7
S:R = 7:9
9S = 7R
9(R7) = 7R
2R = 63
R = 31.5
S = 24.5
S:R = 7:9
9S = 7R
9(R7) = 7R
2R = 63
R = 31.5
S = 24.5
Question 10

The ratio of the age of a man and his wife is 4:3. After 4years, this ratio will be 9:7. If at the time of marriage the ratio was 7:5, then how many years ago were they married?
A

4

B

5

C

6

D

8

Question 10 Explanation:
m : w = 4 : 3
(m+4)(w+4) = 9 : 7
7(m+4) = 9(w+4)
28w/3 + 28 = 9w + 36
w/3 = 8
w = 24
m = 32
(32  x)(24 x) = 7 : 5
x = 4
(m+4)(w+4) = 9 : 7
7(m+4) = 9(w+4)
28w/3 + 28 = 9w + 36
w/3 = 8
w = 24
m = 32
(32  x)(24 x) = 7 : 5
x = 4
Question 11

Father’s age was five times his son’s age 5years ago and will be three times the son’s age after 2yrs. What is the ratio of their present ages?
A

5:2

B

10:3

C

8:3

D

9:4

Question 11 Explanation:
(f  5) = 5(s  5)
(f + 2) = 3(s + 2)
Solving, s = 12 f = 40
F : S = 10 : 3
(f + 2) = 3(s + 2)
Solving, s = 12 f = 40
F : S = 10 : 3
Question 12

A grandfather has 3 grand children. Age difference of the two younger children is 3. The age of the eldest child is 3 times the age of the youngest child and also two years more than the sum of the ages of the other two children. What is the age of the eldest child?
A

15

B

10

C

22

D

18

Question 12 Explanation:
X = 3z
X = y + z + 2
y  z = 3
solving the three equations, x = 15
X = y + z + 2
y  z = 3
solving the three equations, x = 15
Question 13

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?
A

5

B

10

C

15

D

20

Question 13 Explanation:
X+Y = 10+(Y+Z)
X  Z = 10
X  Z = 10
Question 14

The ages of two person Pand Q differ by 14 years. Six years ago, P was thrice as old as Q. Find the present age of Q?
A

13

B

15

C

16

D

18

Question 14 Explanation:
p  q = 14 ......(1)
(p  6) = 3(q  6)
p  3q = 12 .....(2)
solving(1) and (2)
q = 13
(p  6) = 3(q  6)
p  3q = 12 .....(2)
solving(1) and (2)
q = 13
Question 15

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?
A

6

B

7

C

5

D

4

Question 15 Explanation:
Let Ajay’s age be x
His father’s age = x + 32
His sister’s age = x  3
His mother’s age = x3+29 = x+26
Difference between the ages of his parents = (x+32) (x+26)
=> x = 6
His father’s age = x + 32
His sister’s age = x  3
His mother’s age = x3+29 = x+26
Difference between the ages of his parents = (x+32) (x+26)
=> x = 6
Question 16

My brother is 5years elder to me. My father was 30 years of age whrn my sister was born while my mother was 32 years of age when i was born. If my sister was 5years of age when my brother was born, then what was the age of my father when my brother was born?
A

32

B

35

C

37

D

40

Question 16 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+4(x+5) = 35
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+4(x+5) = 35
Question 17

The present ages of A,B,and C are in the ratio 3:5:8. Eight years old, the sum of their ages was 40. Find B’s present age?
A

12

B

20

C

24

D

40

Question 17 Explanation:
Let the present ages of A, B and C be 3x,5x and 8x respectively
(3x8)+(5x8)+(8x8) = 40
16x  24 = 40
2x  3 = 5
x = 8/2 = 4
B’s present age = 5x = 20
(3x8)+(5x8)+(8x8) = 40
16x  24 = 40
2x  3 = 5
x = 8/2 = 4
B’s present age = 5x = 20
Question 18

At the end of 1994, R was half as old as his grandmother. The sum of the years in which they were born is 3844. How old was R at the end of 1999?
A

48

B

55

C

49

D

53

Question 18 Explanation:
Let the age of R in 1994 be x and of his grandma be 2x
Year of R’s birth 1994  x
Year of grandma’s birth 1994  2x
1994  x + 1994  2x = 3844
3x = 3988  3844 = 144
x = 48
Age of R in 1999 = x+5 = 53
Year of R’s birth 1994  x
Year of grandma’s birth 1994  2x
1994  x + 1994  2x = 3844
3x = 3988  3844 = 144
x = 48
Age of R in 1999 = x+5 = 53
Question 19

In 10 years, a will be twice as old as b was 10 years ago. If a now 9 years older than b, the present age of b is?
A

29

B

39

C

48

D

86

Question 19 Explanation:
A+10 = 2(B  10)
A = B+9
Solving two equations,
B+9 = 2B20
B = 39
A = B+9
Solving two equations,
B+9 = 2B20
B = 39
Question 20

Nina is 9 years older than angel two years ago, angel’s age was half that of nina’s. find angel’s present age?
A

10

B

11

C

15

D

18

Question 20 Explanation:
(A2) = (1/2) * (N2)
2A  4 = N  2
2A  4 = A + 9  2
A = 11
2A  4 = N  2
2A  4 = A + 9  2
A = 11
Question 21

Flora is twice tara’s age after 10years tara will be twothird of flora’s age. find flora's present age?
A

10

B

15

C

18

D

20

Question 21 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
(t+10) = (2/3) * (f+10)
3T + 30 = 2F + 20
2F  3T = 10
2*(2T)  3T = 10
T = 10
F = 2T = 20
Question 22

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?
A

12

B

11

C

10

D

6

Question 22 Explanation:
let my present age be x
(x5)+(x5) = (f5)
X+m = f+5
X = f  m + 5
f  m = 6
x = 6+5 = 11
(x5)+(x5) = (f5)
X+m = f+5
X = f  m + 5
f  m = 6
x = 6+5 = 11
Question 23

The sum of the ages of lily and nancy is twice the different of their ages. Find the ratio of nancy’s age to lily’s age?
A

1:3

B

3:1

C

1:2

D

2:1

Question 23 Explanation:
L+N = 2(LN)
L+N = 2L2N
3N = L
N/L = 1/3
N:L = 1:3
L+N = 2L2N
3N = L
N/L = 1/3
N:L = 1:3
Question 24

A boy is 8 years older than his sister. Two years ago he was twice his sister’s age. find his present age?
A

20

B

10

C

18

D

16

Question 24 Explanation:
B = 8+S
(B2) = 2S4
8+S2 = 2S4
S = 10
B = 18
(B2) = 2S4
8+S2 = 2S4
S = 10
B = 18
Question 25

The ages of pooja and deepa are in the ratio 4:5. Four years ago their ages were in the ratio 8:11. Find pooja’s present age?
A

12

B

15

C

14

D

9

Question 25 Explanation:
pooja’s present age = 4x
deepa’s present age = 5x
(4x4) : (5x4) = 8:11
44x  44 = 40x  32
4x = 12
x = 3
4x = 12
deepa’s present age = 5x
(4x4) : (5x4) = 8:11
44x  44 = 40x  32
4x = 12
x = 3
4x = 12
Question 26

A boy said to his friends,”when i was born my father was as oldas i am now “. If his father’s age will be 60 after 6 years find the son’s present age?
A

25

B

33

C

27

D

30

Question 26 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
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
Question 27

A father’s age is two and a half times more than his sons’s age. 5 years ago, he was six times the age of his son. find the father’s present age?
A

35

B

40

C

38

D

31

Question 27 Explanation:
let the son’s present age be x years
Father’s age = x+2.5x = 3.5x
(3.5x5) = 6(x5)
3.5x  5 = 6x  30
2.5x = 25
x = 10
Father’s present age = 35
Father’s age = x+2.5x = 3.5x
(3.5x5) = 6(x5)
3.5x  5 = 6x  30
2.5x = 25
x = 10
Father’s present age = 35
Question 28

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?
A

11

B

14

C

15

D

10

Question 28 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
daughter’s present age = x
3x*x = 363
3x2 = 363
X2 = 121
X = 11
Daughter’s age after 4 years = 15
Question 29

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?
A

12

B

18

C

6

D

15

Question 29 Explanation:
let their present ages be 3x,5xand7x
sum of their ages before 5 years = 3x  5 = 5x  5 = 7x5
15x  15 = 60
Solving, x = 5
Age of the youngest = 3x = 15
sum of their ages before 5 years = 3x  5 = 5x  5 = 7x5
15x  15 = 60
Solving, x = 5
Age of the youngest = 3x = 15
Question 30

The difference between the ages A and C is half the age of B. The difference between the ages of A and B is onesixth of the age of C. If the age of the ages of B and C is 32, find the age of A?
A

25

B

22

C

20

D

27

Question 30 Explanation:
A  C = B/2
A  B = C/6
B+C = 32
Solving the three equation, A = 22
A  B = C/6
B+C = 32
Solving the three equation, A = 22
Question 31

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?
A

18

B

19

C

15

D

21

Question 31 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
(x+y)/2 = 21
x+y = 42
(x+y+z)/3 = 19
x+y+z = 57
42+z = 57
z = 15
Question 32

5 years ago, 1/5^{th} of keith’s age was equal to 1/7^{th} of dora’s age. The average of their present ages is 29. Find keith’s age after 5 years?
A

30

B

39

C

26

D

27

Question 32 Explanation:
(K  5) /5 = (D  5) /7
(K + D) /2 = 29
Solving, k = 25, D = 33
K+5 = 30
(K + D) /2 = 29
Solving, k = 25, D = 33
K+5 = 30
Question 33

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?
A

20

B

25

C

28

D

30

Question 33 Explanation:
A = S+3
S = M+5
A+S+M = 73
S+3+S+S5 = 73
S = 25
S = M+5
A+S+M = 73
S+3+S+S5 = 73
S = 25
Question 34

The present age of ram and raj differ by 7. Five years back, raj was twice the age of ram. Find the age of ram after 4years?
A

16

B

20

C

21

D

25

Question 34 Explanation:
Let raj’s age be x and ram’s age be y
xy = 7
x5 = 2(y5)
solving the two linear equations
y = 12, y+4 = 16
xy = 7
x5 = 2(y5)
solving the two linear equations
y = 12, y+4 = 16
Question 35

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?
A

10

B

12

C

15

D

20

Question 35 Explanation:
V = 8+N
(V/N) = (5/3)
Solving the two equations, N = 12
(V/N) = (5/3)
Solving the two equations, N = 12
Question 36

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?
A

23 years

B

21 years

C

33 years

D

25 years

Question 36 Explanation:
Let his present age be x
X+1 = 2(x=10)
Solving, x = 21
X+1 = 2(x=10)
Solving, x = 21
Question 37

At present, shyam is twice as old as his sister. Three years back, he was thrice her age. find his sister’s percentage age?
A

8

B

9

C

12

D

6

Question 37 Explanation:
Let his sisters present age be x
Shyams present age = 2x
2x3 = 3(x3)
x = 6
Shyams present age = 2x
2x3 = 3(x3)
x = 6
Question 38

On a mans tombstone, it is said that one sixth of his life was spent in childhood and one twelfth as a teenage. 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?
A

48 years

B

42 years

C

70 years

D

84 years

Question 38 Explanation:
Let the mans age be x years and his sons age be y years
(x/6)+(x/12)+(x/7)+5+y+4 = x
x = 2y
By solving, x = 84
(x/6)+(x/12)+(x/7)+5+y+4 = x
x = 2y
By solving, x = 84
Question 39

A father is three as old as his son. After fifteen years the family will be twice as old as his sons age at that time. Hence the fathers present age is?
A

36

B

42

C

45

D

48

Question 39 Explanation:
F = 3S
F+15 = 2(S+15)
By solving equation, F = 45
F+15 = 2(S+15)
By solving equation, F = 45
Question 40

A wizard named nepo says '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?
A

360

B

240

C

120

D

480

Question 40 Explanation:
N = 3S
F = 2N+40
F+N+S = 1240
Solving these, N = 360
F = 2N+40
F+N+S = 1240
Solving these, N = 360
Question 41

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

18

B

16

C

11

D

9

Question 41 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 2years is 18
(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 2years is 18
Question 42

Thirteen years back my mother was thrice my age and two years back, she was twice my age. Find my mothers present age?
A

58

B

46

C

28

D

30

Question 42 Explanation:
Let my age be x and my mothers age be y
y13 = 3(x13)
y2 = 2(x2)
by solving equation, y = 46
y13 = 3(x13)
y2 = 2(x2)
by solving equation, y = 46
Question 43

Ram and raj are twins. The sum of their ages combined with their fathers age is 47. Their fathers age at the time of their birth was 29. Find the age of ram?
A

6

B

9

C

11

D

4

Question 43 Explanation:
R+R+F = 47
FR = 29
By solving two equations, R = 6
FR = 29
By solving two equations, R = 6
Question 44

The sum of ages of a mother and a son is equal and a son is equal to the age of the father. Three years later, the father will b six times as old as his son. The ratio of the present ages of the mother and the son is 10:1. Find the age of the father?
A

27

B

30

C

33

D

36

Question 44 Explanation:
M+S = F
F+3 = 6(S+3)
M/S = 10
Solving these equations, f = 33
F+3 = 6(S+3)
M/S = 10
Solving these equations, f = 33
Question 45

Ram is 5years elder than lakshman who is 4years elder than bharath. The sum of their ages is 61. Find the age of lakshman?
A

25

B

20

C

15

D

16

Question 45 Explanation:
R = L+5
L = B+4
R+L+B = 61
Solving the three equations, L = 20
L = B+4
R+L+B = 61
Solving the three equations, L = 20
Question 46

In a family of four, the average age is 20. The parents age difference is 6 and the siblings age difference is 4. If the ages of the eldest and youngest member differ by 33, findthe age of the youngest member of the family?
A

4

B

6

C

8

D

2

Question 46 Explanation:
Let the age of parents be x and x+6
Let the age of the siblings be y and y+4
X+6y = 33
(x+x+6+y+y+4)/4 = 20
Solving the equations, y = 4
Let the age of the siblings be y and y+4
X+6y = 33
(x+x+6+y+y+4)/4 = 20
Solving the equations, y = 4
Question 47

Two years ago harish was thrice as old as his brother krish. Two years later, harish will be twice as old askrish. Find the age present age of krish?
A

14

B

12

C

8

D

6

Question 47 Explanation:
H2 = 3*(K2)
H+2 = 2*(K+2)
By solving equation , k = 6
H+2 = 2*(K+2)
By solving equation , k = 6
Question 48

The ratio of the age of A and B is 2:3. If B is 3years elser than A, find the age of A after 2years?
A

2

B

4

C

6

D

8

Question 48 Explanation:
Let the age of A and B be 2x and 3x respectively
3x = 2x+3
A = 2x = 6
B = 3x = 9
Age of A after 2 years is 8
3x = 2x+3
A = 2x = 6
B = 3x = 9
Age of A after 2 years is 8
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