3L of milk are drawn from a container containing 30L of milk. It is re

Question

Competition Mode Question

3L of milk are drawn from a container containing 30L of milk. It is replaced by water and the process is repeated 2 times. What is the ratio of milk to water at the end?

A.  \frac{729}{271}

B.  \frac{743}{229}

C.  \frac{81}{19}

D.  \frac{2187}{100}

E.  \frac{813}{19}

ArunSharma12 · Accepted Answer

Formula in use: Final concentration = Initial concentration *  (1- \frac{amount replaced}{total amount})^{n}

Final concentration of milk =  100*(1-\frac{3}{30})^3  =  100*(\frac{27}{30})^3  = 72.9%
concentration of water = 27.1%
milk:water =  \frac{729}{271} 
Ans: A

eakabuah · Answer

We are given that there was a 30L milk in a container. Out of this milk, 3 liters of milk was taken out and replaced with 3L of water. This process of drawing out 3L from the container was repeated twice.
After the first replacement, the amount of milk left  = 30-3=27L  concentration of milk in container =  0.9 
After second replacement the amount of milk left  = 27 - 3*0.9 = 27-2.7 = 24.3L.  Concentration is now  \frac{243}{300} = 0.81 
After third replacement the amount of milk left  = 24.3 - 3*0.81 = 24.3-2.43 = 21.87L . 
Concetration  =\frac{21.87}{30}=\frac{729}{1000} 
Hence for every  729L  of milk there is  (1000-729) = 271L  of water.
So ration of milk to water  = \frac{729}{271}

The answer is therefore A.

nick1816 · Answer

Amount of Milk after 3 Replacements/ Total Volume of the mixture =  (1-\frac{3}{30})^3

Amount of Milk after 3 Replacements/ Total Volume of the mixture =  \frac{729}{1000}

ratio of milk to water at the end = 729 : (1000-729) = 729 : 271

GMATWhizTeam · Answer

Solution: 
 • Initial amount of milk in container = 30 L
• Initial amount of water in container = 0 L
• 3 L of milk is removed and replaced with water
 o Amount of milk in container = 30 – 3 = 27L
o Amount of water in the container = 3L
  Ratio of milk to water =  \frac{27}{3} = \frac{9}{1}   
• Now, again 3L solution is removed from the container.
 o In this case only milk is not removed, water is also removed.
o Milk removed from the container =  \frac{9}{10}*3 = 2.7  L
  Milk left in the container =  27 – 2.7 = 24.3  L 
o Water removed from the container =  \frac{1}{10}*3 = 0.3 
  Water left in the container =  3 – 0.3 = 2.7  L
 Water in the container after the addition of 3 litre water =  2.7+3 = 5.7  L 
o Ratio of milk to water =  \frac{24.3}{5.7} . 
• Now, 3L solution is replaced with water one more time
 o Milk removed =  \frac{24.3}{30}*3 = 2.43 
  Milk left in the solution =  24.3 – 2.43 = 21.87  L 
o Water removed = \frac{5.7}{30}*3=0.57L 
  Water left =  5.7 – 0.57 = 5.13  L
Water in container after the addition =  5.13+3=8.13   
• Ratio of milk to water =  \frac{21.87}{8.13} = \frac{2187}{813}=\frac{729}{271}  
Hence, the correct answer is  Option A.

unraveled · Answer

3L of milk are drawn from a container containing 30L of milk. It is replaced by water and the process is repeated 2 times. What is the ratio of milk to water at the end?

A. 729/271

B. 743/229

C. 81/19

D. 2187/100

E. 813/19

After removing 3L of milk 3L of water is added. So the mixture has Milk to Water ratio of 9:1. Milk is 27L and Water is 2.7L. Now the process is repeated again so 3L of the mixture is removed. 
Removed mixture has water content of 0.3L and Milk content of 2.7L. Total milk content left =  24.3 L. As 3L of water is added total water content is 2.7 + 3 =  5.7 L
Ratio of Milk to Water =  \frac{24.3}{5.7}  =  \frac{81}{19}

Answer C.

Gulliksona · Answer

Gotta add up to a whole number no math needed but each time factor out 10% off the next calculation.

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exc4libur · Answer

con_final=con_initial(vol_intial-pure/vol_initial)^3
x=100%milk(30-3/30-3+3)^3
x=(27/30)^3=(3^3/3*10)^3=3^9/3^3*10^3
x=3^6/10^3=729/1000=milk/total
milk/water=729/(1000-729)=729/271

ans (A)

minustark · Answer

3L of milk are drawn from a container containing 30L of milk. It is replaced by water and the process is repeated 2 times. What is the ratio of milk to water at the end?

Formula for such questions is Ratio of mlk:total =n (1-replaced quantity/total quantity)^(number of times) = \((1-\frac{3}{30})^3=(\frac{9}{10})^3=729/1000\).
So water = 1000-729=271
Thus milk:water=\(\frac{729}{271}\)

A

5.7 +2.43) =21.87 : 8.13 = 7.29 : 2.71 A is the answer.

freedom128 · Answer

Worthy question!

Although not necessary for this specific question, I will do generalization to such typical MIXTURE PROBLEM so that you can solve similar, but harder question (eg. repeated 10x etc.)

Process #1:  (30-3) litre wine left = 30*(1-1/10) = 30*(9/10)^1 litre wine left, total 30L;

#2:  {30*(9/10)^1} - {30*(9/10)^1}/30*3L= 30*(9/10)*(1-1/10) = 30*(9/10)^2 litre wine left, total 30L;

... etc

I clearly see now following patterns when process are repeated  N times : 
Wine left =30*(9/10)^N
Water content =30*{1-(9/10)^N}

N=2 
Wine left =30*(9/10)^2 =30*(81/100)
Water content =30*{1-(9/10)^2} = 31*(19/100)
---> Wine to water ratio 
= 30*(81/100) / {30*(19/100)} 
= 81/19

FINAL ANSWER IS (C)

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daagh · Answer

The ratio of milk: water after two repeats is 24L Milk and 6L water, 24/6 or four times. The closest answer is only C, which is 81/19. However, I am not clear why the option 24/6 is not given as an answer.

firas92 · Answer

10% of a 100% solution of milk is replaced with water thrice

Final concentration of milk=100%*(9/10)*(9/10)*(9/10)=72.9%

Final concentration of water=100-72.9=27.1%

Ratio=729/271

Answer is (A)

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monikakumar · Answer

Ans C
milk proportion intially = 1;
after adding water, mp reduces = 27/30=9/10
when it is done twice = 1*9/10*9/10=81/100
final mp is 81/100
so mp:wp = 81:19

chetan2u · Answer

3L of milk are drawn from a container containing 30L of milk. It is replaced by water and the process is repeated 2 times. What is the ratio of milk to water at the end?

Formula for such questions is Ratio of mlk:total =n (1-replaced quantity/total quantity)^(number of times) =  (1-\frac{3}{30})^3=(\frac{9}{10})^3=729/1000 .
So water = 1000-729=271
Thus milk:water= \frac{729}{271}

A

yashikaaggarwal · Answer

30 litre milk - 3litres of milk + 3 litres of water.
27:3= milk : water - litre mixture
27-2.7:3-0.3= 24.3:2.7
+ 3 litre water.
24.3:5.7
- 3 litre of mixture.
24.3-2.43 : 5.7-0.57
21.87 : 5.13
Add 3 litre of water
21.87:8.13
2187/813
729/271
OA is A

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lacktutor · Answer

After the first process, 
—>  27L  —milk 
—>  \frac{27}{30} = \frac{9}{10}= 0.9L  milk in 1L mixture

After 2nd process 
—>  27 —3*0.9= 27–2.7 = 24.3L  milk 
—>  \frac{24.3}{30} L milk in 1L mixture

After 3rd process, 
—>  24.3 —3*\frac{24.3}{30} = 24.3 —2.43 = 21.87L  milk 
 30 —21.87 = 8.13 L water 
—>  \frac{milk}{water} = \frac{21.87}{8.13} = \frac{2187}{813} = \frac{729}{271}

Answer ( A)
 
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monikakumar · Answer

I really cannot get this..the process is done only twice right, why are we doing it thrice?

Bunuel · Answer

For me "...repeated 2 times" means that something was done once and then repeated 2 more times.

monikakumar · Answer

So this is how we have to view this question in GMAT also?..is this how GMAT also interpret?

freedom128 · Answer

I will do generalization to this typical mixture problem so that we can solve similar, but harder question (eg. repeated 100x etc.)

Process #1:  (30-3) litre milk left = 30*(1-1/10) = 30*(9/10)^1 litre milk left, total 30L;

#2:  30*(9/10) - 30*(9/10)*(3L/30) = 30*(9/10)*(9/10) = 30*(9/10)^2 litre milk left, total 30L;

...etc

Now, I clearly see patterns when process are repeated N times:
Milk left =30*(9/10)^N
Water content =30*{1-(9/10)^N}

When N=3, 
Milk left =30*(9/10)^3 =30*(729/1000)
Water content =30*{1-(9/10)^3} = 31*(271/1000)
So, milk to water ratio
= 729/271

FINAL ANSWER IS (A)

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3L of milk are drawn from a container containing 30L of milk. It is re

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