There are two vessels A and B. Vessel A is containing 40 litres of pur

Question

There are two vessels A and B. Vessel A is containing 40 litres of pure milk and vessel B is containing 22 litres of pure water. From vessel A, 8 litres of milk is taken out the poured into vessel B. Then 6 litres of mixture (milk and water) is taken out the from vessel B poured into vessel A. What is the ratio of the quantity of pure milk in vessel A to the quantity of pure water in vessel B?

(A) 24 : 17
(B) 13 : 7
(C) 21 : 11
(D) 14 : 5
(E) 3 : 1

(A) 24 : 17
(B) 13 : 7
(C) 21 : 11
(D) 14 : 5
(E) 3 : 1

JerryAtDreamScore · Answer

Breaking Down the Info:

From vessel A, 8 litres of milk is taken out the poured into vessel B:

Now vessel A has 32 L of milk. Vessel B has 8 L milk and 22 L water, hence 30 L of  \frac{8}{30} = \frac{4}{15}  percent milk.

Then 6 litres of mixture (milk and water) is taken out the from vessel B poured into vessel A:

This is one-fifth of vessel B taken out; among that we have  6*\frac{4}{15} = \frac{8}{5} = 1.6 	ext{ L}  milk and  6 - 1.6 = 4.4  L water.

Then vessel A has 32 + 1.6 = 33.6 L of milk. Vessel B has 22 - 4.4 = 17.6 L of water.

33.6 : 17.6 = 168:88 = 21:11

Answer: C

IanStewart · Answer

Not sure of the source, but in case it's one of your questions and comments would be helpful -- there's a typo in the stem, but more importantly, I don't think there's any such thing as 'pure milk', the way this question uses the phrase. Milk is mostly water, along with some other things, which makes it confusing to mix 'pure milk' with water. When people talk about 'pure milk', they mean milk without impurities, and not what this question means. So I'd use something other than milk in a question like this.

Bunuel · Answer

Thank you Ian. Not my questions. My questions usually come under GMAT Club Tests tag.

lucasd14 · Answer

A_0 = 40_m --> A_1 = 32_m --> A_2 = 32_m + 6*(32/30w + 8/30m)  
 B_0 = 22_w --> B_1 = 22_w + 6_m --> B_2=22_w + 8_m - 6*(32/30w + 8/30m)

Now we need to consider only the milk for A and only the water for B:
 A_m = 32 + 6*32/30 
 B_w = 22 + 6*8/30

\frac{A_m}{B_w} = (32 + 6*32/30) / (22 + 6*8/30) = \frac{2*21}{22} = \frac{21}{11}

IMO: Option C

Francesco_8167 · Answer

What can we infer the mixture of 6 liter is proportional to the total amount of 30 liters from? (and not, for example, made of 5liters milk and 1liter water)

Sorry to disturb, but with gmat questions i mostly feel that inferring is wrong because they state everything that is not common sense, and sometimes that they imply something that could have various nuances like in this case (if i am not missing something - which indeed is quite likely).

Thanks!!

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There are two vessels A and B. Vessel A is containing 40 litres of pur

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There are two vessels A and B. Vessel A is containing 40 litres of pur

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