Aptitude question and answer on Problems on age

In this section we are going to discuss about problems on age problems. Not just the overview of the topic, but also you are going to learn the important formulas on problems on age along with explanation which is easy to understand.

1
Santosh is four times as old as his son. four years later the sum of their ages will be 43 years. The present age of son is
A.    5 years
B.    7 years
C.    8 years
D.    10 years

Answer : B.   7 years

Explanation:
Let son's age = x
then, Santosh's age =4x 
\(\dot{..}\) (x+4)+(4x+4)=43
x=7
\(\dot{..}\)Present age of the son = 7 years.

2
Ten years ago, P was half of Q's age. If the ratio of their present ages is 3:4, what will be the total of their present ages?
A.    30
B.    35
C.    40
D.    45

Answer : B.   35

Explanation:
Let the present age of P and Q be 3x and 4x respectively.

Ten years ago, P was half of Q's age
=> (3x – 10) = \(1\over2\)(4x – 10)
=> 6x – 20 = 4x – 10
=> 2x = 10
=> x = 5

total of their present ages = 3x + 4x = 7x = 7 × 5 = 35

3
A man's age is 125% of what it was 10 years ago, but \(83\dfrac{1}{3}\%\) of what it will be after 10 years. What is his present age?
A.    40
B.    50
C.    60
D.    70

Answer : B.   50

Explanation:
Let the age before 10 years = x

Then \(125x \over100\) = x + 10

=>125x = 100x + 1000

=> x = \(1000 \over 25\) = 40

Present age = x + 10 = 40 +10 = 50

4
Present ages of Kiran and Syam are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Syam's present age in years ?
A.    24
B.    25
C.    26
D.    27

Answer : A.  24

Explanation:
Ratio of the present age of Kiran and Syam = 5 : 4

Let the present age of Kiran = 5x 
Present age of Syam = 4x

After 3 years, ratio of their ages = 11:9
=> (5x + 3) : (4x + 3) = 11 : 9
=> 9(5x + 3) = 11(4x + 3)
=> 45x + 27 = 44x + 33
=> x = 33-27 =6

Syam's present age = 4x = 4×6 = 24

5
Five years ago, the total of the ages of a father and his son was 40 years. The ratio of their present ages is 4 : 1. What is the present age of the father ?
A.    30 years
B.    20 years
C.     25 years
D.    None of these

Answer : D.  None of these

Explanation:
Let son's age = x. Then father's age = 4x
\((x-5)+(4x-5)=40\)
\(⇒x = 10\)
Present age of father = 40 years

6
One year ago Jaya was four times as old as her daughter Nikitha.  Six years hence, Mrs.Jaya's age will exceed her daughter's age by 9 years. The ratio of the present ages of Jaya and her daughter is :
A.    9 : 2
B.    11: 3
C.    12: 5
D.    13: 4

Answer : D.  13: 4

Explanation:
Let Nikitha's age 1 year ago = x
Then Jaya's age 1 year ago = 4x
After 6 years their ages are \(4x+7, x+7\)
\((4x+7) - (x+7) = 9 \) or \(x = 3\)
Present age of Jaya = (12+1) years = 13 years
Present age of Nikitha = (3+1) years = 4 years
Ratio of their ages = 13 : 4



7
The sum of the ages of a mother and daughter is 50 years. Also, 5 years ago, the mother's age was 7 times the age of the daughter. The present ages of the mother and daughter respectively are :
A.    35 years, 15 years
B.    38 years, 12 years
C.    40 years, 10 years
D.    42 years, 8 years

Answer : C.  40 years, 10 years

Explanation:
Let the daughter's present age be x years. Then, mother's present age = (50-x) years.

Now, \(7(x-5)=(50-x-5)\) or \(x = 10\)

So, their present ages are 40 years and 10 years. 

8
The sum of the ages of a son and father is 56 years. After 4 years, the age of the father will be three times that of the son. Their ages respectively are:
A.    12 years, 44 years
B.    16 years, 42 years
C.    16 years, 48 years
D.    18 years, 36 years

Answer : A.  12 years, 44 years

Explanation:
Let the present ages of son and father be x years

and \((56-x) \) years respectively.

Then \((56-x+4)=3(x+4)\)

or 4x =48 or x = 12

So their ages are 12 years, 44 years respectively.