Age problems

          1)      Father is aged three times more than his son. After 8 years he would be two and a half of his son’s age. After further 16 years how many times would he be of his son’s age?

Solution:-  assume that the son’s present age is x years and father’s present age

=x+3x=4x years

After 8 years their ages will be x+8 and 4x+8

4x+8=(5/2)*(x+8)…….(given)

4x-5x/2=20-8

3x/2=12

è x=8

Therefore, son’s present age=8 years and fathers present age=32

(8+16) years their ages will be,

Son’s age=32 and father’s age=56

èfather’s age=7/4 of son’s age

     2)      The sum of ages of 6 children born at the interval off 2 years is 60 year. What is age of the youngest child?

Solutions:- assume that the age of the youngest child is x years

Age of the 2^nd child=x+2

Age of the 3^rd child=(x+2)+2=x+4

 Age of the 4^th child=(x+4)+2=x+6

Age of the 5^th child=(x+6)+2=x+8

Age of the 6^th child=(x+8)+2=x+10

Therefore, x+x+2+x+4+x+6+x+8+x+10=60

6x+30=30 è 6x=30 è x=5

Hence the youngest child is 5 years old.

     3)      Karan’s father was 30 years old when he was born. And his mother was 26 years old when his sister was born who is 3 years younger than him.What is the difference between his parent’s ages?

Solution:- assume that karan’s age is x years

Today	4 years ago
Karan=4                         <==	Karan=0
Father=34                        <==	Father=30
Sister=0
Mother=26                        è	Mother=22

Difference=34-26=30-22=8 years

      4)      If we subtract 8 from grandfather’s present age and divide the remainder by 15 we get the present age of grandson who his 3 years younger than his brothers of 7 years. Find the present age the grandfather?

Solution;- assume that the present age of grandfather is x years.

(x-8)/15=4 è x=60+8=68

Grandfather’s age=68 years

      5)      If after 10 years A will be thrice as old as B was 10 years ago. If A is now 4 years elder than B then what is the present age of B?

Solution:- assume that the present age of B is x years.

	10 years ago	Present ages	10 years later
A	(x+4)-10=x-4	x+4	(x+4)+10=3(x-10)
B	x-10	x	x+10

X+14=3x-30

14+30=3x-x

44=2x

X=22 years

6) If 6 years is subtracted from A's age and the remainder is divided by 8 then B's age is obtained. If Jasmine is 2 years younger than C who is 9 then what is the age of A ? 

Solution;- Assume that the A's age is x years.

According to condition given, we have

(x-6)/8= B's age = 9-2 = 7 years

(x-6)/8=7 ==> x=7*8+6=60 years

7) Manish was as old as his daughter Jasmine at the time of his birth. If the present age of Manish is 32 years then what will be the age of Jasmine 4 years ago?

       Solution:- Assume that the present age of Jasmine is x years. Now we get
    

Jasmine's birth	Manish= x	Jasmine= 0
Present ages	Manish=32	Jasmine= x

From the above table we have,

 32-x=x-0

 32=2x

16=x

4 years ago she will be 12 years old.