Question

. in a family, average ages of father and son, father and mother, and mother and son are 25,40 and 24 respectively. what is the age of the son in years a)9 b)9.5 c)10 d)10.5 next

Answer 1

Let the age of father, mother ans son are f, m and s years respectively.
According to question:
(f+s)/2 = 25 => f+s = 50 ---  (i)
(f+m)/2 = 40 =>f+m = 80 ---(ii)
(m+s)/2 = 24 => m+s = 48  ---(iii)
Subtracting eq^{n} [/tex] (iii) from (ii),
f-s = 32 -----(iv)
Adding eq^{n} [/tex] (i) from (iv),
2f = 82 => f = 41
Substituting value of f in  eq^{n} [/tex] (i), we will get
s = 9

Hence, age of son is 9 years.
Ans: a

Answer 2

Solution :-

Let the ages of son, father and mother be x, y and z respectively.

Then, according to the question.

⇒ (x + y)/2 = 25

⇒ x + y = 25*2

⇒ x + y = 50 ........................(1)

⇒ (y + z)/2 = 40

⇒ y + z = 2*40

⇒ y + z = 80 .........................(2)

⇒ (z + x)/2 =24

⇒ z + x = 48 ..........................(3)

Now, subtracting (1) from (2).

         y + z = 80
   x + y       = 50
  -   -            -   
_______________
 - x       + z = 30
_______________

  z - x = 30 .............(4)

Now, subtracting (4) from (3)

      z + x = 48
      z - x  = 30
     -  +      -
_____________
        2x  = 18
_____________

⇒ 2x = 18

⇒ x = 18/2

⇒ x = 9

Hence, the age of son is 9 years.

So, the option (a) is correct.