A vessel contains milk and water in the ratio 3:2. The volume of the

Question

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 From this solution 30 litre of the mixture is withdrawn and then replaced with water.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?

A. 65 L
B. 75 L
C. 77 L
D. 80 L
E. 82 L

A. 65 L
B. 75 L
C. 77 L
D. 80 L
E. 82 L

Ned · Accepted Answer

Hey - here's another approach, hope it helps.

Ratio of milk to water = 3:2...so we can take the volume of milk to be 3V and the volume of water to be 2V, and the total volume to be 3V + 2V = 5V.

Volume is increased by 50% by adding water. Therefore volume goes from 5V to 7.5V (an increase of 2.5V). Since only water has been added the NEW volume of water in solution is now 2V + 2.5V = 4.5V.

And the new ratio of milk to water is 3:4.5

Now 30 liters are withdrawn. Since we know the new ratio we can calculate that the volume of milk withdrawn is (30/7.5)*3 = 12 liters, which means 18 liters of water have been withdrawn (30 liters in total, minus 12 liters of milk).

Resultant volume of milk = 3V -12

Resultant volume of water = 2V + 2.5V -18 + 30
(Remember 30 liters of solution have been withdrawn, 18L milk and 12L water, and replaced with 30 liters of just water).

The ratio of these two will equal 3:7.

Solving: (3V-12)/(4.5V +12) = 3/7

V = 16 & the original volume is 5V = 5*16 = 80.

Please let me know what you think of this approach. Didn't take long at all.

KarishmaB · Answer

The problem isn't very tough if your understand your mixtures well. 
Work with each statement one by one.

Step 1: 
"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 =  /(2+1) = 2/5
Say the volume of this final mixture is V litres.

Step 2:
"From this solution 30 litres of the mixture is withdrawn and then replaced with water.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.

Step 3:
"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

jrymbei · Answer

I understood both the method by Ned and Karishma but the approach mentioned by Ned seems to more easy to interpret. Kudos to both of you for your help.

Just want to know is there any good guide where I can have better concept on mixtures where volume and concentrations are involved. I am having tough time to resolve this kind of problem.

Besides, do you think this kind of problems are for higher scoring, I mean is this problem is of good standard or we can expect more tougher then this one.

KarishmaB · Answer

This problem is definitely not very easy but it has been made tough by adding steps to it. Also, you need to re-trace the steps to get to 80 lts. That makes it a little time consuming and tedious. GMAT generally does not give you long tedious questions though they are tricky. The moment the trick clicks, you need 30 secs to solve the question. There is a fun element in the actual GMAT questions - they make you think hard, not calculate a lot.

jrymbei · Answer

I agree with you Karishma. Is there any guide for quick tricks. I had a long way to go to bring myself to a competent level.To me it's like a never ending story, I need real good score since my acad was not worth mentioning :cry:

Lots of studies needs to be done.

ottomankhan · Answer

Let the amount of milk was 3x and water was 2x.

after adding 50% water milk becomes 3x and water becomes (2x + 50% of 5x) = 4.5x.... total voulme of mixture now is 7.5x and new ratio 3:4.5 = 6:9

applying method of allegation,

6/15....................1
...........7/10.........
3/10................1/10
3....................1

7.5x -30 / 30 = 3/1

7.5x = 120 
5x = 120*5/7.5 = 80

Posted from my mobile device

exc4libur · Answer

milk/total=3/5=60%
add water = 0.5*total
milk/(total+0.5total)=3(7.5)=40%
final milk concentration=30%
30%=40%(v-30/v-30+30),
.3v=.4v-12, v=120
v final = 120 = 1.5 v initial
v initial = 120/1.5 = 80

Ans (D)

satya2029 · Answer

Let say solution is 5X
after addition of water it becomes=5X+5X*(0.5)=7.5X=3X(milk)+4.5X(Water)
after 30 litre of the mixture is withdrawn and then replaced with water, water quantity will be
4.5X-30*3/5+30( why 3/5... because the ratio is (3/4.5)=2/3,so water/Mix=3/5)
4.5X+12
which equals to 7Y
4.5X+12=7y or 9X+24=14Y
and
7.5X=10Y this gives 3X=4Y or 9X=12Y
Y=12
X=16
5X=80
D:)

Mugdho · Answer

M : W=> 3:2
after increasing 50%, M:W=> 2:3=>6:9
final ratio of of M : W => 3:7=>6:14
(14-9)=>5=30
So, 1=>6L
so after adding 50%, volume=> (90+30=120L)
Original volume=> 120*100/150=80L

Posted from my mobile device

cpucci · Answer

Hey! Just a quick thought that I would appreciate if somebody could check if it makes sense, because it makes the exercise less than a minute long.

First, as we first know that the ratio is 3:2, we know that the total volume has to be divisible by 5, therefore we discard answer choices C & E (77L and 82L).

After adding the extra volume (50% in total), it has to be divisible by 10 (given the final ratio of 3:7). Therefore, we need to find a number divisible by 5, that when increased by 50%, is divisible by 10. Therefore, we discard options A & B (65L and 75L).

Therefore, the only answer choice that fills this checks is D, 80L.

Thanks

KarishmaB · Answer

You can use this method to arrive at a "likely" answer quickly and move on if you don't have time, but it is not necessary that each ingredient in a solution must have an integer volume. 
Say I could easily have 33 litres of 20% milk solution. We don't expect difficult calculations because of limited time and hence expect easy integer  numbers but that is not necessary.

bumpbot · Answer

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