A milkman mixed 4 litres of water with 10 litres of milk. He boiled on

Question

A milkman mixed 4 litres of water with 10 litres of milk. He boiled one fourth of this mixture till the water content in it, halved. Then he added it to remaining mixture. What is the proportion of milk in the mixture after the process?

A. 7/10

B. 20/27

C. 21/27

D. 18/15

E. 19/15

A. 7/10

B. 20/27

C. 21/27

D. 18/15

E. 19/15

EgmatQuantExpert · Answer

Given  :
 • A milkman mixed 4 liters of water with 10 liters of milk.
• He boiled one-fourth of this mixture till the water content in it halved.
 o Then he added it to the remaining mixture.

To find  :
 • The proportion of milk in the mixture after the process.

Approach and Working out  :

The volume of solution after mixing 4 liters of water with 10 liters of milk =14L

¾ of the solution that is kept as it is:
 • Volume of solution that was not taken out = 14 - 3.5 = 10.5L.
 o Milk and water in solution is in the ratio of 10:4 = 5:2 
• Hence, quantity of milk in ¾ of the solution =  \frac{5}{7}  × 10.5 =7.5L
 o Quantity of water in ¾ of the solution =  \frac{2}{7}  × 10.5 =3 L

¼ of this solution that is taken out.
 • Volume of solution taken out = 14/4 = 3.5 L.
 o Milk and water in 3.5L solution is in the ratio of 10:4 = 5:2 
• Hence, quantity of milk in ¼ of the solution =  \frac{5}{7}   × 3.5 =2.5L
 o Quantity of water in ¼ of the solution =  \frac{2}{7}  × 3.5 =1 L

This 3.5L of the mixture is boiled until the water quantity becomes half.
 • New quantity of milk = Old quantity of milk = 2.5 L
• New quantity of water = ½ of 1 L = 0.5L

Now, this mixture is added to the original solution again.
 • Total quantity of milk = 7.5 + 2.5 = 10L
• Total quantity of water = 3+0.5 = 3.5L

The proportion of milk after the process =  \frac{10}{13.5}  =20/27
Hence, option B is the correct answer.

Correct Answer: Option B

TestPrepUnlimited · Answer

One-fourth of the content:   1 L  of water and 2.5 L of milk.

After boiling:   0.5 L  of water and 2.5 L of milk.

So we can see from this boiling process, all that happened was 0.5 L of water was boiled and milk did not change.

Then we are left with 3.5 L water and 10 L milk. The proportion of milk is  \frac{10}{13.5} = \frac{20}{27}

Ans: B

astiles67 · Answer

There are 2 grammatical problems with this question that can lead to wrong answers.

"He boiled one fourth of this mixture till the water content in it, halved."

1. We do not know if this means that he took 1/4 OUT of the prior mixture or if is is an additional mixture that would be 1/4 of the prior mixture.

2. Water and milk can boil. It is ambiguous as to whether the water AND milk boil in half, or if just the water boils in half while the milk stays the same.

I do understand why GMAT questions intentionally make ambiguous directions.

argerniki · Answer

+1

While I think that the 1st point is clear (" He boiled one fourth  of this mixture  till the water content in it, halved. "), I made the same mistake and halved the proportion of milk in the part that was boiled down as well. 
An additional explanation ("Note: milk has a higher boiling point than water") would clear up the ambiguity.

Ilanchezhiyan · Answer

Took a long time to solve this. Any easier ways to sovle this?

A milkman mixed 4 litres of water with 10 litres of milk. He boiled on

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