Home ≫ Arithmetic Aptitute ≫ Problems based on Ages ≫ Page 1
1. The age of the father 3 years ago was 7 times the age of his son. At present the father's age is five times than that of his son. What are the present ages of the father and the son?
  A.   Father's age: 40 years; Son's age: 8 years
  B.  Father's age: 45 years; Son's age: 9 years
  C.   Father's age: 50 years; Son's age: 9 years
  D.   Father's age: 45 years; Son's age: 5 years
     
   
View Answer

Shortcut:
If 'm' years earlier the father's age was 'q' times that of his son. At present the father's age is 'n' times that of his son. Then the present ages of the son and the father are
m(q − 1) / q − n
and n
[
m(q − 1) / q − n
]
respectively.
Here, m = 3, q = 7, n = 5
Using these values in the shortcut, we get:
Son age =
3(7 − 1) / 7 − 5
=
3 x 6 / 2
= 9
Hence, son age is 9 years.
Father's age = n
[
m(q − 1) / q − n
]
= 5 x 9 = 45 years

2. 12 years ago, the ratio of the ages of Deepa and Disha was 2 : 3. If there present ages ratio is 5 : 6, what will be the total of their present ages.
  A.   44 years
  B.   40 years
  C.  54 years
  D.  45 years
     
   
View Answer

Shortcut:
If 'm' years earlier the father's age was 'q' times that of his son. At present the father's age is 'n' times that of his son. Then the present ages of the son and the father are
m(q − 1) / q − n
and n
[
m(q − 1) / q − n
]
respectively.
Here, m = 12, q =
2 / 3
, n =
5 / 6

Using these values in the shortcut, we get:
12(2/3 − 1) / 2/3 − 5/6
=
12 x (− 1/3) / − 1/6
=
− 4 / − 1/6
= 4 x 6 = 24 years
Hence, son age is 9 years.
Father's age = n
[
m(q − 1) / q − n
]
=
5 / 6
x 24 = 20
Hence, sum of their ages = 24 + 20 = 44 years.

3. The age of Ramesh's father is 4 times his age. if five years ago, father's age was 7 times of the age of his son at that time. What is Ramesh's father's present age?
  A.  50 years
  B.  40 years
  C.  45 years
  D.  40 years
     
   
View Answer

Shortcut:
If 'm' years earlier the father's age was 'q' times that of his son. At present the father's age is 'n' times that of his son. Then the present ages of the son and the father are
m(q − 1) / q − n
and n
[
m(q − 1) / q − n
]
respectively.
Here, m = 5, q = 7, n = 4
Using these values in the shortcut, we get:
Father's age = 4
[
5(7 − 1) / 7 − 4
]
= 4
[
5 x 6 / 3
]
= 4 x 5 x 2 = 40
Hence, age of father = 40 years.

4. At present the age of the father is five times than that of the ageo of his son. Three years hence, the father's age would be four times that of his osn. Find the present ages of the father and the son.
  A.  Father's age: 40 years; Son's age: 8 years
  B.  Father's age: 50 years; Son's age: 10 years
  C.  Father's age: 40 years; Son's age: 8 years
  D.  Father's age: 45 years; Son's age: 9 years
     
   
View Answer

Shortcut:
If the present age of the father is 'n' times the age of his son. 'm' years hence/after, the father's age becomes 'q' times the age of his son. Then the present ages of the son and father are
m(q − 1) / n − q
and n
[
m(q − 1) / n − q
]
respectively.
Here, m = 3, q = 4, n = 5
Using these values in the shortcut, we get:
Father age = 5
[
3(4 − 1) / 5 − 4
]
= 5
[
3 x 3 / 1
]
= 5 x 9 = 45
Hence, age of father is 45 years.
Son's age =
3(4 − 1) / 5 − 4
= 3 x 3 = 9
Hence, age of son is 9 years.

5. The ratio between the present ages of M and N is 5 : 8. After four years, the ratio between their ages will be 2 : 3. What is N's present age?
  A.  32 years
  B.  33 years
  C.  30 years
  D.  35 years
     
   
View Answer

Shortcut:
If the present age of the father is 'n' times the age of his son. 'm' years hence/after, the father's age becomes 'q' times the age of his son. Then the present ages of the son and father are
m(q − 1) / n − q
and n
[
m(q − 1) / n − q
]
respectively.
Let M is son and N is father.
then, father's age (N) is
8 / 5
times of Son (M)
N =
8 / 5
M
or n =
8 / 5

Similarly, after 4 years
N =
3 / 2
M
or q =
3 / 2

So, n =
8 / 5
, m = 4, q =
3 / 2

Using these values in the shortcut, we get:
Father age =
8 / 5
[
4(3/2 − 1) / 8/5 − 3/2
]

=
8 / 5
[
4(3 − 2)/2 / (16 − 15)/10
]

=
8 / 5
[
2 / 1/10
]
=
8 / 5
x 2 x 10 = 32
Hence, age of father is 32 years.

6. The age of Raju is four times the age of his son. After ten years the age of Raju will be only twice the age of his son. Find the present age of Raju's son.
  A.  8 years
  B.  5 years
  C.  10 years
  D.  4 years
     
   
View Answer

Shortcut:
If the present age of the father is 'n' times the age of his son. 'm' years hence/after, the father's age becomes 'q' times the age of his son. Then the present ages of the son and father are
m(q − 1) / n − q
and n
[
m(q − 1) / n − q
]
respectively.
Here, m = 10, q = 2, n = 4
Using these values in the shortcut, we get:
Son's age =
10(2 − 1) / 4 − 2
=
10 / 2
= 5
Hence, age of son is 5 years.

7. Three years earlier the father was 7 times as old as his son. Three years hence the father's age would be four times that of his son. What are the present ages of the father and the son?
  A.  None of these
  B.  35 years
  C.  32 years
  D.  45 years
     
   
View Answer

Shortcut:
If t1 years earlier the age of the father was 'q' times the age of his son. t2 years hence, the age of the father becomes 'n' times the age of his son. Then
The present age of the son =
t2(n − 1) + t1(q − 1) / q − n
and
The present age of the father =
[
son's age / 2
(n + q) −
t1 / 2
(q − 1) +
t2 / 2
(n − 1)
]
years respectively.
if t1 = t2 = t, then the Son's present age =
t(q + n − 2) / q − n
and
Father's present age =
[
son's age / 2
(q + n) −
t / 2
(q − n)
]

Here, t1 = t2 = 3, q = 7, n = 4
Using these values in the shortcut, we get:
Son's present age =
3(7 + 4 − 2) / 7 − 4
=
3(7 + 2) / 3
= 9
Hence, age of son is 9 years.
Father's present age =
[
9 / 2
(7 + 4) −
3 / 2
(7 − 4)
]

=
[
9 / 2
(7 + 4) −
3 / 2
(7 − 4)
]

=
[
9 / 2
x 11 −
3 / 2
x 3
]
=
[
99 − 9 / 2
]
=
[
90 / 2
]
= 45
Hence, the age of father is 45 years.

8. One year ago the ratio between Dinesh's and Zahir's age was 4:3. One year hence the ratio of their ages will be 5 : 4. What is the sum of their present ages in years?
  A.  14 years
  B.  18 years
  C.  16 years
  D.  20 years
     
   
View Answer

Shortcut:
If t1 years earlier the age of the father was 'q' times the age of his son. t2 years hence, the age of the father becomes 'n' times the age of his son. Then
The present age of the son =
t2(n − 1) + t1(q − 1) / q − n
and
The present age of the father =
[
son's age / 2
(n + q) −
t1 / 2
(q − 1) +
t2 / 2
(n − 1)
]
years respectively.
if t1 = t2 = t, then the Son's present age =
t(q + n − 2) / q − n
and
Father's present age =
[
son's age / 2
(q + n) −
t / 2
(q − n)
]

One year ago Dinesh's age was
4 / 3
of Zahir's age.
One year hence Dinesh's age will be
5 / 4
of Zahir's age.
So, t1 = t2 = 1, q =
4 / 3
, n =
5 / 4

Using these values in the shortcut, we get:
Zahir's present age =
1(4/3 + 5/4 − 2) / 4/3 − 5/4

=
(16 + 15 − 24)/12 / (16 − 15)/12

=
(31 − 24)/12 / 1/12

=
7/12 / 1/12
=
7 x 12 / 12
= 7
Hence, age of Zahir is 7 years.
Now, by the first relation:
D − 1 / 7 − 1
=
4 / 3

D − 1 / 6
=
4 / 3

D − 1 = 6 x
4 / 3

D = 8 + 1 = 9
Dinesh age is 9 years.
Sum of Dinesh & Zahir age is (9 + 7) years = 16 years

9. Ten years ago Manish was thrice as old as Zakir was but 10 years hence, he will be only twice as old as Zakir. Find the present age of Manish
  A.  70 years
  B.  30 years
  C.  60 years
  D.  75 years
     
   
View Answer

Shortcut:
If t1 years earlier the age of the father was 'q' times the age of his son. t2 years hence, the age of the father becomes 'n' times the age of his son. Then
The present age of the son =
t2(n − 1) + t1(q − 1) / q − n
and
The present age of the father =
[
son's age / 2
(n + q) −
t1 / 2
(q − 1) +
t2 / 2
(n − 1)
]
years respectively.
if t1 = t2 = t, then the Son's present age =
t(q + n − 2) / q − n
and
Father's present age =
[
son's age / 2
(q + n) −
t / 2
(q − n)
]

Ten year ago Manish's age was 3 times of Zahir's age.
Ten year hence Manish's age will be 2 times of Zahir's age.
So, t1 = t2 = 10, q = 3, n = 2
Using these values in the shortcut, we get:
Zahir's present age =
10(3 + 2 − 2) / 3 − 2
= 30
Hence, age of Zahir is 30 years.
Now, by the first relation:
M − 10 / 30 − 10
= 3
M − 10 / 20
= 3
M − 10 = 3 x 20
M = 60 + 10 = 70
Manish age is 70 years.

10. 10 years ago Renu's mother was 4 times older than Renu. After 10 years, the mother will be twice older than Renu. What is the present of Renu?
  A.  25 years
  B.  20 years
  C.  22 years
  D.  24 years
     
   
View Answer

Shortcut:
If t1 years earlier the age of the father was 'q' times the age of his son. t2 years hence, the age of the father becomes 'n' times the age of his son. Then
The present age of the son =
t2(n − 1) + t1(q − 1) / q − n
and
The present age of the father =
[
son's age / 2
(n + q) −
t1 / 2
(q − 1) +
t2 / 2
(n − 1)
]
years respectively.
if t1 = t2 = t, then the Son's present age =
t(q + n − 2) / q − n
and
Father's present age =
[
son's age / 2
(q + n) −
t / 2
(q − n)
]

Ten year ago Mother's age was 4 times of Renu's age.
Ten year hence Mother's age will be 2 times of Zahir's age.
So, t1 = t2 = 10, q = 4, n = 2
Using these values in the shortcut, we get:
Renu's present age =
10(4 + 2 − 2) / 4 − 2
=
40 / 2
= 20
Hence, age of Renu is 20 years.

Copyright © 2020-2022. All rights reserved. Designed, Developed and content provided by Anjula Graphics & Web Desigining .