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Aptitude question and answer on Problems on age



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.