Arithmatical -Problems on Ages

DIRECTIONS : Problems based on Ages.
1. Present ages of Sameer and Anand are in the ratio of
5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
  A.   24
  B.   27
  C.  40.
  D.   cannot be determined
Solution
Let the present ages of sameer and anand be 5x years and 4x years respectively.
Then5x+3/4x+3=11/9
≈9(5x+3)=11(4x+3)
x=6.
Anands's present age = 4x
=24 years.
2. The ratio between the present ages of P and Q is 5 : 7 respectively. If the difference between Q's present age and P's age afler 6 years is 2, what is the total of P's and Q's present ages?
  A.  46 years
  B.  48 years
  C.  52 years
  D.  56 years
Solution
Let the present ages of P and Q be 5x years and 7x years respectively.
Then7x-(5x+6)=2
2x=8
x=4.
Required sum= 5x+7x
=12x
=12×4
=48 years.

3. Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old as his son. Then the sum of the present ages of the son and the father is
  A.  54.
  B.  72
  C.  105
  D.  108
Solution
Let the present ages of Father and Son be 2x years and x years respectively.
Then(2x-18)=3(x-18)
2x-18=3x-54
x=54-18
x=36.
Required sum= (2x+x)
=3x
=3x36
=108 years.
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