Guys, Here's another problem I found while practicing today. Initially I was not able to figure out the problem itself and it took a long time to resolve this one..
A vessel contains milk and water in the ratio 3:2. The volume of the contents is increased by 50% by adding water to this. From this solution 30 litre of the mixture is withdrawn and then replaced with water. The resultant ratio of milk to water in the final solution is 3:7. Find the original volume of the solution?
Also, please update how much time it took to resolve the problem. I want to check my level..whether it is really difficult and time consuming or not.
The problem isn't very tough if your understand your mixtures well.
Work with each statement one by one.
Check out these post to understand the equations used: http://www.veritasprep.com/blog/2011/03 ... -averages/http://www.veritasprep.com/blog/2011/04 ... -mixtures/
"A vessel contains milk and water in the ratio 3:2. The volume of the contents is increased by 50% by adding water to this."
You have milk:water = 3:2
volume of this solution:volume of water added = 2:1 (Since volume is increased by 50%)
Let's focus on milk. Solution 1 with 3/5 milk is mixed with solution 2, which has no milk, in the ratio 2:1
Fraction of milk in final mixture of step 1 = [(3/5)*2 + 0*1]/(2+1) = 2/5
Say the volume of this final mixture is V litres.
"From this solution 30 litres of the mixture is withdrawn and then replaced with water. "
This just means that (V - 30) lt of our final mixture above is mixed with 30 lt of water.
"The resultant ratio of milk to water in the final solution is 3:7. "
This tells us that when we mix V-30 lt of mixture in which milk is 2/5 with 30 lt water, we get fraction of milk = 3/10
(V - 30)/30 = (0 - 3/10)/(3/10 - 2/5)
We get V = 120 lt
Since V was the volume of the final mixture in step 1, the volume of solution 1 in step 1 must have been 80 lt (because when you increase it by 50% i.e. 40 lt, you get 120 lt)
The original volume of the solution = 80 lt
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