A vessel contains 80 L milk. The milkman delivers 20L to the first hou

Question

A vessel contains 80 L milk. The milkman delivers 20L to the first house and adds an equal quantity of water. He does exactly the same at the second and third house. What is the ratio of milk and water when he has finished delivering at the third house ?

(A) 61 : 64
(B) 49 : 51
(C) 41 : 44
(D) 27 : 37
(E) 18 : 19

Are You Up For the Challenge: 700 Level Questions

(A) 61 : 64
(B) 49 : 51
(C) 41 : 44
(D) 27 : 37
(E) 18 : 19

Are You Up For the Challenge: 700 Level Questions

shah999 · Accepted Answer

Milk : Water
 80

-20

60 : 20

Milk final=initial (1- removed/initial)^n n=no. of times removed

Milk final=80(1-20/80)^3

80x27/64

135/4

water final= 80-135/4
 
 185/4

MILK : Water

135/4 : 185/4

27 : 37

option (D)

ThatDudeKnows · Answer

The total is always 80 at the end of each house, so if we just keep track of the amount of water, we can figure out the amount of milk at the end.

Start with 0 water.

At first house, add 20 water. --> 20 water.

At second house, remove 1/4 of the mixture, so remove 5 water. Then add 20 water. --> 35 water.

At third house, remove 1/4 of the mixture, so remove 35/4 water. Then add 20 water. --> 35+20-(35/4) = 55-(35/4)=(220-35)/4 = 185/4 water.

Total is 320/4. 185/4 is water. So 135/4 is milk.

We are asked for milk:water. 135:185 = 27:37.

Answer choice D.

Nidzo · Answer

What is happening here is a geometric progression, for which the formula is  a_n = ar^{(n-1)} .

As we are working towards a ratio, set  a = 100 . This is because we start with 100% milk and then progressively are adding water (0% milk).

r = \frac{3}{4}  as we have 80l of liquid and are constantly removing 20l of liquid.

n = 4  as we need to include delivery and the addition of water afterwards (essentially what will the mixture be once delivering to a hypothetical fourth house).

Putting this all together gives us (working out % of milk):  100 * (\frac{3}{4})^3

100 * \frac{27}{4*4*4}

25 * \frac{27}{16}

\frac{675}{16}  % of milk

Let water = w. Now because the mixture of milk and water has to amount to 100% and there is a denominator of 16 in the % of milk, one can go:

\frac{675}{16}+\frac{w}{16} = \frac{1600}{16}

Multiply through by 16

675 + w = 1600

w = 975

Water:Milk =  975:675  
Divide through by 25
Water:Milk =  27:37

Answer D

azamatboden · Answer

ThatDudeKnows , why do you remove 1/4 of mixture?

ThatDudeKnows · Answer

azamatboden

Each time the milkman arrives at a house, he has 80L in his vessel and he delivers 20L. 20 is 1/4 of 80. So, he delivers 1/4 of everything in the vessel. Does that make sense?

TK0697 · Answer

A vessel contains 80 L milk. The milkman delivers 20L to the first house and adds an equal quantity of water. He does exactly the same at the second and third house. What is the ratio of milk and water when he has finished delivering at the third house ?

(A) 61 : 64
(B) 49 : 51
(C) 41 : 44
(D) 27 : 37
(E) 18 : 19

Are You Up For the Challenge: 700 Level Questions

The milkman removes 20L out of 80L, which is 1/4 of the total. This means 3/4 of the milk remains after each house.

Since milkman does this removal 3 times, then we multiple 3/4 three times so we can find how much milk is left after third time = (3/4)x(3/4)x(3/4) = 27/64

This fraction 27/64 means 27 portion is milk out of total 64 portions.

Question ask ration of Milk to Water. We already know milk portion is 27. To find water, is total portion 64 - milk portion 27 = water portion 37.

Answer of milk to Water = 27:37 Answer D

OrbitNerd · Answer

Quick method:

The vessel starts with 80 L and 20 L is removed each time, so after each delivery, the fraction of milk left is:

80-20/80=3/4

This process happens 3 times, so the fraction of milk remaining is:
27/64 (cubing 3/4)

Thus, out of 64 parts of the final mixture:

Milk = 27 parts
Water = (64-27=37) parts

Therefore:

Milk:Water=27:37

KarishmaB · Answer

Use the concept of replacement discussed here:  https://anaprep.com/arithmetic-replacement-in-mixtures/

Cf = Ci * (\frac{Vi}{Vf})^n = 1 * (\frac{60}{80})^3 = \frac{27}{64}  (Concentration of milk in the mix)

Concentration of water  = 1 - \frac{27}{64} = \frac{37}{64}

Ratio of milk : water = 27:37

Answer (D)

A vessel contains 80 L milk. The milkman delivers 20L to the first hou

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A vessel contains 80 L milk. The milkman delivers 20L to the first hou

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