Practice
Series for IBPS Exams: Problems on Ages
1. The ratio of the present age of Anamika to that
of Sharmita is 13 : 17. Four years ago the ratio of their ages was 11 : 15.
What will be the ratio of their ages six years hence?
Solution:
Let the present ages of
Anamika and Shamita be 13x and 17x respectively.
Then,
(13x-4) /(17x-4) = 11/15
2. A’s age is twice C’ age. Ratio of age of B 2
years hence to age of C 2 years ago is 5 : 2. C is 14 years younger than D.
Difference in ages of D and A is 4 years. Find the average of their ages.
Solution:
A = 2C
(B+2)/(C-2) = 5/2
C = D – 14
D – A = 4
Solve, A = 20, B = 18, C
= 10, D = 24
3. The ratio of the present age of Anu to that of
her mother is 1 : 2. The ratio of their ages 6 years hence would be 11:20. What
was the ratio of their ages 9 years ago?
Solution:
Let the present age of
Anu be x years and the present age of her mother be 2x years.
Then,
x +6/ 2x+6 = 11 / 20
After solving, x = 27
Age of Anu 9 years ago =
27 – 9 = 18 years
Age of Anu’s mother 9
years ago = 54 – 9 = 45 years
Reqd ratio = 18 : 45 = 2
: 5
4. Sambhu is 6 times old as Tinku. Sambhu's age
will be twice that of Umesh after 10 years. If Umesh's 13th birthday was
celebrated 3 years ago what will be Sambhu's age after -6 years?
Solution:
Umesh’s present age = 13
+ 3 = 16 years
Sambhu’s age after 10
years =2 x (16 + 10) = 52 years
Sambhu’s present age = 52
— 10 = 42 years
Sambhu’s age after 6
years = 42 + 6 = 48 years
5. The average age of 70 girls in a classroom is
20 years . The average age of a group of 15 girls in the classroom is 18 years
and the average age of another 30 girls in the classroom is 15 years . What is
the average age of the remaining girls in the classroom?
Solution:
70 * 20 = 15*18 + 30*15 +
25*x
=> 1400 = 270 + 450 +
25*x
=> 1400 – 720 = 25*x
=> 680 /25 = x = 27.2
years
6. The average age of a family of 6 members is 22
years. If the age of the youngest member be 7 years. What was the average age
of family at the birth of the youngest members?
Solution:
6 * 22 = 132 , 6 * 7 = 42
132 – 42 = 90/5 = 18
years
7. At present, Aruna's age is 1.5 times the age of
Pujan and twice the age of Somy. After six years, Aruna will be 1.4 times the
age of Pujan and Somy will be 0.8 times the age of Pujan then, what is the
present age of Somy?
Solution:
Let Pujan’s present age
be 
years.
years.
Aruna’s present age
= 
years
years
Therefore, Somy’s
present age = 1.5x/2 years
After six years,
Pujan’s age = x +
6 years
Aruna’s age = 1.5x +
6 years
Now, 1.4 (x + 6) = 1.5x
+ 6 => 1.4x + 8.4 = 1.5x + 6 => 0.1x = 2.4 => x = 24 years
Somy’s present age =
1.5*24/2=18 = 18 years
8. The respective ratio between the present ages
of father, mother and daughter is 7 : 6 : 2. The difference between mother’s
and the daughter’s age is 24 years. What is the father’s age at present?
Solution:
Let the common ratio be x
∴ The percentages of father’s, mother’s and daughter’s are 7x, 6x, 2x respectively.
According to the question
6x ⎯ 2x – 24
4x = 24
x = 6
∴ father’s present age
= 7 × 6 = 42 years
9. The present ages of Vishnu and Vinoth are in
the ratio of 14 : 17 respectively. 6 yr from now, their ages will be in the
ratio of 17 : 20, respectively. What is Vinoth’s present age?
Solution:
V/S = 14/17
V = 14S / 17
Again,
(V + 6)/(S + 6) = 17/20
20V + 120 = 17S + 102
20×(14S/17) +120 = 17S
+102
(280S/17) + 120 = 17S +
102
120 – 120 = (17S –
280S)/17
18 = (280S – 280S)/17
S = 34yr
10. The ages of two persons differ by 15 years. 7
years ago, the elder one was 4 times as old as the younger one. What are their
present ages of the elder person?
Solution:
Let present age of the elder
person = x and
present age of the
younger person = x−15
(x – 7) = 4 (x – 15 – 7)
x – 7 = 4x – 88
3x = 81
x = 27
11. Jitendra’s age is three times the sum of the
ages of his two sons. Two years ago, his age was six years less than four times
the sum of the ages of his sons. What is the present age of Jitendra?
Solution:
Let the sum of Jitendra’s
sons be x years
Then, Jitendra’s age = 3x
Again, 4(x – 2) – 6 = 3x
– 2
or, 4x – 8 – 6 =3x – 2
or, x = 12 years
Present age of Jitendra =
3 x 12 = 36 years
12. At present, the ratio of the ages of A to B is
3 : 8; and that of A to C is 1 : 4. Three years ago, the sum of the ages of A,
B and C was 83 years. What is the present age (in years) of C?
Solution:
According to the
question, A : B = 3 : 8
A : C = 1 : 4
B : A = 8 : 3
A : C = 1 : 4
8 : 3 : 12
Sum = 8x + 3x 12x = 23x
Now, 23x = 92
x = 4
Hence the present age of
C = 12x = 12 x 4 = 48 years
13. Atif's age is 1/6th of his father's age.
Atif's father, Kayyum’s age will be twice the age of Ravi's age after 10 years.
If Ravi's tenth birthday was celebrated three years before, then what is Atif's
present age.
Solution:
Let present age of Ravi =
r
Then we have r = 10 + 3 =
13 years as Ravi’s 10th birthday was three years ago
Now, we have Ravi’s age
after 10 years = r + 10 = 13 + 10 = 23
Let the present age of
atif and kayyum be a and k respectively.
Then we have
k + 10 = 2 × (10 + r)
=> k + 10 = 2 × 23 => k = 46 – 10 = 36
Hence, age of Atif = k/6
= 36/6 = 6 years
14. The sum of ages of family members (both
children and parents) is 360 years. The total ages of children and parents are
in the ratio 2:1 and the ages of wife and husband are in the ratio 5:7.What
will be the age of husband?
Solution:
Sum of ages is 360 years.
The ratio of children and parents ages is 2:1.
Total age of parents =
360 x 1 / 3 = 120 years
Ratio of wife and husband
age is 5:7. Therefore, the age of husband = 120 x 7 / 12 = 70
Hence the age of husband
is 70 years.
15. If 6 years are subtracted from the present age
of Anuj and the remainder is divided by 18, then the present age of his
grandson Gopal is obtained. If Gopal is 2 years younger to Mohan whose age is 5
years, then what is the age of Anuj?
Solution:
Let Anuj’s age be X
Gopal is 2 years younger
than Mohan, so Gopal is 3 years (i.e 5 – 2 = 3)
If Arun had born 6 years
before, his age would had been X – 6. As per the question, X – 6 should be 18
times as that of Gokul’s age.
i.e. (X – 6) /18= 3
X-6 =3 x 18
x = 60
16. At present Sheetal is three times Surabhi’s
age. After seven years Sheetal will be twice Surabhi’s age then. How many times
will Sheetal’s age be in another fourteen years time with respect to Surabhi's
age then ?
Solution:
Surabhi’s present age = x
years
Sheetal’s present age = 3x
years
After seven years,
3x + 7 = 2(x +
7)
Þ 3x + 7 = 2x +
14
Þ x = 7
Therefore, Surabhi’s
present age = 7 years
Sheetal’s present age =
21years
After another 14 years
i.e. after 21 years
Surabhi’s age = 28 years
Sheetal’s age = 42 years
Therefore, Required
answer = 42/28 = 1.5
17. At present, Tarun is twice the age of Vishal
and half the age of Tanvi. After Four years, Tarun will be 1.5 times Vishal age
and Tanvi will be 2.5 times Vishal age, what is Tanvi present age?
Solution:
Let Tanvi’s age be x
years
Therefore, Trun’s age =
x/2 and Vishal’s age is x/4 years
After four years,
(x + 4) = (x/4 + 4) × 2.5
=> x+ 4 = 2.5x/4 + 10 => 4x + 16 = 2.5x + 40 => 1.5x = 24
=> x = 24/1.5 = 16 .
18. Farah was married 8 years ago. Today her age
is 1 2/7 times to that at the time of marriage. At present her daughter’s age
is 1/6 th of her age. What was her daughter’s age 3 years ago?
Solution:
Let Farah’s age 8 years
ago be x years
Farah’s present age = (x
+ 8) years
Therefore, x + 8 = 9x/7
=> 7x + 56 = 9x => 2x = 56 => x = 28
Farah’s present age = 28
+ 8 = 36 years
Her daughter’s age 3
years ago = 36 × 1/6 = 6 years
19. 12 yr ago the ratio between the ages of A and
B was 3 :4 respectively. The present age of A is 3 ¾ times of C's present age.
If C's present age is 10 yr, then what is B's present age?
Solution:
(A + 12)/(B + 12) = 3/4
and A = 15/4 C => A = 15/4 × 10 = 37.5
(37.5 + 12)/(B + 12) =
3/4 => 4 × 49.5 = 3B + 36 => 3B = 198 – 36 => B = 162/3 = 54
Therefore Present age of
B = 54 years
20. In a family, a couple has a son and daughter.
The age of the father is three times that of his daughter and the age of the
son is half of his mother. The wife is nine years younger to her husband and
the brother is seven years older than his sister. What is the age of the
mother?
Solution:
Let the mother’s age be y
years.
Therefore, The age of
father = (y + 9) years
The age of son = y/2
years
The age of daughter =
(y/2 – 7)years
ATQ, (y + 9) = 3 (y/2 –
7) => y + 9 = 3y/2 – 21 => y/2 = 30 => y = 60
Therefore age of Mother =
60 years.
