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There are two identical containers A & B. The container A contains 1

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There are two identical containers A & B. The container A contains 1  [#permalink]

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New post 15 Feb 2020, 18:23
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A
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GMATBusters’ Quant Quiz Question -6


There are two identical containers A & B. The container A contains 1 Litre pure water and container B contains B 1 litre of pure milk. Now 5 cups of water container A taken out and is mixed well in container B. Then, 5 cups of this mixture is taken out and mixed in the container A. If M denotes the proportion of milk in the container A and N denote the proportion of water in container B, then:
A. M<N
B. M>N
C. M=N
D. 2M= N
E. Info insufficient, can’t be determined.

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Re: There are two identical containers A & B. The container A contains 1  [#permalink]

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New post Updated on: 15 Feb 2020, 19:31
There are two identical containers A & B. The container A contains 1 Litre pure water and container B contains B 1 litre of pure milk. Now 5 cups of water container A taken out and is mixed well in container B. Then, 5 cups of this mixture is taken out and mixed in the container A. If M denotes the proportion of milk in the container A and N denote the proportion of water in container B, then:
Let a cup is equal to 100ml = 1/10 of the litre
hence A quantity after 5 cups of water is taken out = 1 - 5*100= 0.5 litre
B quantity after 5 cups of water is added = 1 + 0.5litre ( 1 litre milk & 0.5litre= water)
Now 5 cups of mixture is taken out from B, so B quantity becomes 1 litre but proportion of milk and water remains unchanged which is N= proportion of water = 0.5/(1.5)=1/3
A water quantity becomes = 0.5litre + 0.5/3 = 2/3 and milk quantity is 0.5*2/3 = 1/3
hence proportion of milk = (1/3)/1 = 1/3

hence M= if M denotes the proportion of milk in the container A = 1/3
hence M= N

lets say when 800ml = 0.8 litre is taken out so A quantity after 5 cups of water is taken out = 0.2
B quantity= 1.8 litre but proportion of water in mixture= 0.8/1.8= 4/9
N = proportion of water in container B= 4/9
A quantity after 0.8 litre is now taken from mixture B = 1 litre and proportion of milk = 0.8*5/9= 4/9
M= if M denotes the proportion of milk in the container A = 4/9

hence C is the answer

Originally posted by pk123 on 15 Feb 2020, 18:39.
Last edited by pk123 on 15 Feb 2020, 19:31, edited 2 times in total.
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Re: There are two identical containers A & B. The container A contains 1  [#permalink]

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New post 15 Feb 2020, 18:44
Here the ratio of mixtures( i.e milk , water) doesnot matter. But the important point is that whether the total amount ( either pure or mixture ) being transferred is equal or not. Since the total amount ( i.e 5 cups) being transferred from each one to another , hence A =B.

So, C is the answer.
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Re: There are two identical containers A & B. The container A contains 1  [#permalink]

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New post 15 Feb 2020, 19:15
There are two identical containers A & B. The container A contains 1 Litre pure water and container B contains B 1 litre of pure milk. Now 5 cups of water container A taken out and is mixed well in container B. Then, 5 cups of this mixture is taken out and mixed in the container A. If M denotes the proportion of milk in the container A and N denote the proportion of water in container B, then:
A. M<N
B. M>N
C. M=N
D. 2M= N
E. Info insufficient, can’t be determined.

Answer - C

We can have any proportion of 5 cups mixed in other container, the result will be container A having same % of milk as in container B having water

For eg. we take 500 ml (for 5 cups) of water mixed with milk -> Result will 1.5 ltrs having 0.5 ltr of water giving concentration of 0.5/1.5 => 1/3 => N = 33.33% of water

So 500 ml of this concentration will contain 2/3 of 500 ml of milk => 33.33% milk in 500 ml

When we add 500 ml of this concentration in 500 ml of water -> result will be 33.33% milk in 1 ltr of mixture => M

Therefore M = N

Similarly,

If we take 200 ml (for 5 cups) then 200 ml of water mixed in 1 ltr of milk -> 0.2 ltr water in 1.2 ltr of mixture -> 0.2/1.2 =1/6 concentration of water = N

When we mix 200 ml of this concentration => 5/6 of 200 ml added to 500 ml of water => 1000/6 in 1 ltr mixture => 1/6 of milk => M

Again M=N.
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Re: There are two identical containers A & B. The container A contains 1  [#permalink]

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New post 15 Feb 2020, 19:45
A 0% 1litre water
B 100% 1litre milk

if 5cups is equal to 0.9litre
proportion of milk in B is 100%*1+0%*0.9=x*1.9 x=52.6%, N=100%-52.6%=47.4%
proportion of milk in A is 0%*0.1+52.6%*0.9=M*1 M=47.4% N=M

if 5cups is equal to 0.1litre
proportion of milk in B is 100%*1+0%*0.1=x*1.1 x=90.9%, N=100%-90.9%=9.1%
proportion of milk in A is 0%*0.9+90.9%*0.1=M*1 M=9.1% N=M

in any measurement of 5cups M and N are equal so C is right
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Re: There are two identical containers A & B. The container A contains 1  [#permalink]

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New post 15 Feb 2020, 22:22
container A (water) = 1000 ml
container B (milk) = 1000 ml

let the capacity of 1 cup = 100 ml

now 5 cups of water (that is 500 ml) is taken out from A and is mixed with B
the concentration of A and B after the process

container A = 500 ml
container B - milk = 1000 ml water = 500 ml---ratio of milk to water = 2:1

now 5 cups of mixture (that is 500 ml) is taken out and mixed with A
milk and water taken out will be in ratio 2:1
let 2t of milk and t water is taken out from B

500 = 3t
t = \(\frac{500}{3 }\)
water taken out from B = \(\frac{500}{3}\) ml
milk taken out from B = \(\frac{1000}{3}\) ml

the concentration of A and B after the process

container A - milk = \(\frac{1000}{3}\) ml water = \(\frac{2000}{3}\) ml

ratio of milk : water = 1:2
proportion of milk in container A = \(\frac{1}{3}\) = M

container B - milk = \(\frac{2000}{3}\) ml water = \(\frac{1000}{3}\) ml

ratio of milk : water = 2:1
proportion of water in container B = \(\frac{1}{3}\) = N

from here we get M = N

C is the answer
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Re: There are two identical containers A & B. The container A contains 1  [#permalink]

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New post 16 Feb 2020, 01:06
Solution:

Question 6: There are two identical containers A & B. The container A contains 1 Litre pure water and container B contains B 1 litre of pure milk. Now 5 cups of water container A taken out and is mixed well in container B. Then, 5 cups of this mixture is taken out and mixed in the container A. If M denotes the proportion of milk in the container A and N denote the proportion of water in container B, then:

A. M<N
B. M>N
C. M=N
D. 2M= N
E. Info insufficient, can’t be determined.

In this question, we need to find out how the proportion of milk or N in A relates to the proportion of water in B after the transfer of mixture from B to A..

Information given in the question: Water in A = Milk in B = 1 litre.
First transfer: First 5 cups of water from A to B makes remaining quantity in A = 1 litre - 5 cups of water
Let 1 cup measures x litres. Then, 5 cups = 5x litres. Thus, quantity in A = \(1 - 5x\) litres.
Moreover, resulting mixture in B after the transfer = 1 litre milk + 5 cups of water (from A). Total quantity of mixture in B = \(1 + 5x \)litres.

Second transfer: 5 cups of mixture from B to A. Therefore, resulting quantity in B would be reduced to 1 litre again and quantity in A too would increase from \(1 - 5x\) to 1 litre. However, B is a mixture of water and milk before the second transfer. The mixture contains 1 litre milk and 5x litres water. Thus, if quantity of 5x is transferred from the mixture in B to A, then resulting ratios of milk to water can be calculated by:


Proportion of milk in B = \(\frac{1}{(1 + 5x)}\).
Proportion of water in B = \(\frac{5x}{(1 + 5x)}\).
Proportion of milk in B after transfer of 5x cups to A = \(1 - \frac{1*5x}{(1 + 5x)}\) = \(\frac{1}{(1 + 5x)}\)
Quantity of milk transferred = \(\frac{5x}{(1 + 5x)}\)

Proportion of water in B after transfer of 5x cups to A = N = \(5x - \frac{5x*5x}{(1 + 5x)}\) = 5x/1 + 5x
N can be written as \(\frac{5x}{1}\) as the total quantity remaining in B after the transfer is 1 litres.

The proportion of milk in A after the transfer or M = \(\frac{5x}{(1 - 5x + 5x)}\) or \(\frac{5x}{1 }\) as the total quantity in A after the addition of 5x litres or 5 cups is \(1 - 5x + 5x or 1\) litres.

Thus, \(M = N = \frac{5x}{1}\) and option C is the right answer.
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Re: There are two identical containers A & B. The container A contains 1  [#permalink]

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New post 16 Feb 2020, 05:35
I had to think about this for some time.
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Re: There are two identical containers A & B. The container A contains 1   [#permalink] 16 Feb 2020, 05:35

There are two identical containers A & B. The container A contains 1

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