Problems on Ages

Problems on Ages :-
Example 1. :- The ratio of present ages of Ram and his father is 2:9 . The father's age
                    at time of Ram's birthday was 28 years.the present ages of the father and Ram.
Explanation :- Let the present ages of Ram and his father is 2x and 9x
                        Ram age = father age -28
                            2x=   9x-28
                            7x = 28
                              x = 4
                        Hence  present ages of Ram and his father is 8 and 36.
     
Example 2. :-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 that of his son. What are the

                       present ages of the father and son?

Explanation :- Let the present age of son and father are x  and 5x . 

                       Three years ago  age of son and father are x-3  and 5x-3 .                      

                        7(x – 3) = 5x – 3

                         7x – 21 = 5x – 3

                         2x = 18

                       Hence, son’s age = 9 yrs.  Fathers’ age = 45 years.                        

Example 3. :-The age of father is thrice that of his son. After 12 years,

                       the age of the father will be twice that of his son. What is the

                        present age of the son and father?

Explanation :- Let the present age of son and father are x  and 3x . 

                       After 12 years age of son and father are x+12  and 3x+12.                      

                        3x+12 = 2(x+12)

                         x = 12

                       Hence  present ages of son and his father is 12 and 36.

Example 4. :-The ratio between Ram and Shyam ages are 5:6 respectively.

                       After 10 years the ratio between age of Ram and  Shyam’s age will be

                       7:8. Then what is Shyam’s present age?

Explanation :- Let the present ages of Ram and Shyam are 5x and 6x

                        After 10 years age of Ram and Shyam are 5x + 10 and 6x + 10

                         (5x+10)/(6x + 10) = 7/8

                          40x + 80 = 42x + 70

                           2x = 10

                             x = 5 

                         Hence  present ages of Ram and Shyam are 25 and 30.

Example 5. :-The product of the ages of Ram an Shyam is 240.If the twice the age of Shyam is 4                                year more to Ram age.Then what is Ram’s present age?

Explanation :- Let the present ages of Ram is x 

                        Then Shyam age 240/x

                        2*240/x = x + 4

                         x²+4x = 480

                         x²+4x -480 = 0

                         x²+24x - 20x -480= 0

                         x(x+24) - 20(x+24) = 0

                         x=-24, x=20

                         Hence  present ages of Ram and Shyam are 20 and 12.

Example 6. :-The sum of ages of 5 children born at the intervals of 3 years each is 50 years. 

                       What is the age of the youngest child?

Explanation :- Let the  ages of children are x,x+3,x+6,x+9,x+12.

                       x+(x+3)+(x+6)+(x+9)+(x+12) = 50

                       5x + 30 = 50

                       5x = 20

                       x = 4

                       Hence age of the youngest child = 4

Example 7. :-A father said to his son, "I was as old as you are at the present 

                      at the time of your birth". If the father's age is 38 years now, the son's age

                      five years back was?

Explanation :-Let the son's present age be x years. 

                      Then x years before father age  (38 - x)

                        (38-x)   = x

                           2x = 38.

                             x = 19.

                       Son's age 5 years back (19 - 5) = 14 years.

Example 8. :-Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5.

                       Four years hence, the ratio of their ages will be 11 : 10. 

                      What is Sagar's age at present?

Explanation :-Let the ages of Kunal and Sagar  6 years ago be 6x and 5x .

                       Present ages of Kunal and Sagar  are 6x +6 and 5x+6 years

                       4 years hence ages of Kunal and Sagar will be 6x +6+4 and 5x+6 + 4.

Then,	(6x + 6) + 4	=	11
	(5x + 6) + 4		10

                       10(6x + 10) = 11(5x + 10)

                         5x = 10

                         x = 2.

                       Hence Sagar's present age = (5x + 6) = 16 years.