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9 liters are drawn from a bowl full of water and is then filled with milk. 9 liters of mixtures are drawn and the bowl is again filled with milk. The quantity of water now left in the bowl is to that of the milk in it as 16:9. How much that the bowl hold????????????
Answers (1)
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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.