Aptitude: Problems On Ages for [clerk and p.o]

Problems on ages is really a complicated part in aptitude test since they take more time compared to that of the other problems we see. Normally people solve these problems with a direct method or they just skip this question. Yet every problems have a shortcut solution method to solve them, so do this. here i gonna give some formula and along with some examples to solve them.lets see it below..

Before we start, there are four formulas used for these problems based on their type. all you have to do is to identify the question type and apply the formula to get the answers in time..

Type 1: 

            't' years earlier, the father's age was x times that of his son. At present  the father's age is Y times that of his son. what are the present ages of father and his son? .

Shortcut  Formula:  for son's age     =      t (x-1) / x-y

                                    for father's age =      y t (x-1) / x-y  ,  that's it

TYPE 1 EXAMPLE :

                       10 years ago, my mother was four times older than me . now my mother will be twice older than me. what is my present age.?

shortcut method:

son's age = 10 (4-1)/ 4-2 =   10 / ans

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Type 2:

               The present age of father is 'Y' times the age of his son. After 't' years, the father's age is 'z' times the age of his son. present age of father and son?

Shortcut formula :  son's age    = (z-1)t / y-z

                                              father's age =  y t (z-1)/ y-z

 TYPE 2 EXAMPLE : 

The age of a man is 4 times of his son. 5 years ago , the man was nine times as old as his son. calculate their ages ?

Shortcut method : z=9 , t=5 , y=4

son's age is  = 5(9-1)/ 9-4 = 8

father's age is = (4*5)(9-1)/(9-4)= 32 

(or)

since father's age is 9 times as son's age, therfore 4*8= 32 .

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Type 3:

             't2' years earlier the age of the father was 'X' times the age of his son. 't2' years later, the age of the father becomes 'Z' times the age of son. what is the present age of father and son?

Shortcut Formula: 
son's age    = [t2(z-1)+ t1(x-1)] / (x-z)
Father's age = t1(z-1) + t1 (x-1)

TYPE 3 EXAMPLE :

Five years before the fathers age was 7 times of his son's age. 5 years hence , father's age 3 times the age of his son. find their present age?

Short cut method :  t1= 5, t2=5, x= 7, z= 3

son's age = [5(3-1)]+5(7-1)] / 7-3 = 10
father's age =  10(7-3) = 40


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Type 4:
                  The ratio of both father and son's age at the present is X:Y . 't' years before the ratio was A:B what is their present age?

Shortcut Formula: 
son's age    = y*[t(a-b)/x*b-a*y]
Father's age = x*[t(a-b)/x*b-a*y]

TYPE 4 EXAMPLE :

the age of you and me are in the ratio 9:4. seven years hence ratio of our ages will be 5:3. find our present age?

Short cut method :

son's age =  4*[7(5-3) / (9*3) - (5*4)] = 8
father's age =  9*[7(5-3) / (9*3) - (5*4)] = 18