Doubt & Answer Explanation

Answer Explanation

Let us say that the volume of bowl = V liters
  In the first case 9 liters of water are drawn out and replaced by milk.
    Water in the bowl =  V-9  and  Milk  =  9 liters.  
 So the ratio of milk to water in the mixture = 9/(V-9)   or Milk : Mixture = 9/V
Again 9 liters of mixture are drawn out
 So milk in this 9 liter mixture  = 9 x  9/V 
   Amount of milk left  = 9 - 81/V
 But also 9 liters of milk are added.
 So the new qty of milk in the mixture = 9 - 81/V + 9  = 18 - 81/V
Total qty of mixture in the bowl remains V liters
 milk/Mixture = (18 - 81/V)/V 
Given :  water : milk = 16: 9 
        milk : water = 9:16
    or  milk : mixture = 9 : 25
     9/25 = (18 -81/v)/v
  this equation reduces to   v² - 50v + 225 = 0
  This gives :  v² - 45v - 5v + 225 = 0
                          (v-45)(v-5) = 0
            Either V = 45 or  V = 5
        But V cannot be equal to 5 , because already we are removing 9 liters out of the bowl
 So volume of bowl = 45 liters.