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

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Manager
Joined: 09 Apr 2017
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Location: Nepal
Concentration: Finance, Entrepreneurship
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3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

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Updated on: 04 Sep 2018, 03:46
1
4
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Difficulty:

55% (hard)

Question Stats:

65% (02:37) correct 35% (02:13) wrong based on 43 sessions

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3L of milk are drawn from a container containing 30L of milk. It is replaced by water and the process is repeated 2 times more. What is the ratio of milk to water at the end?
$$a. \frac{2187}{100}$$
$$b. \frac{81}{19}$$
$$c. \frac{729}{271}$$
$$d. \frac{743}{229}$$
$$e. \frac{813}{19}$$

Originally posted by pratik2018 on 04 Sep 2018, 02:29.
Last edited by chetan2u on 04 Sep 2018, 03:46, edited 1 time in total.
Corrected the question
Math Expert
Joined: 02 Aug 2009
Posts: 7986
Re: 3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

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04 Sep 2018, 02:40
1
pratik2018 wrote:
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?
$$a. \frac{2187}{100}$$
$$b. \frac{81}{19}$$
$$c. \frac{729}{271}$$
$$d. \frac{743}{229}$$
$$e. \frac{813}{19}$$

Although there is a formula but this can be calculated easily ..
After first change 27 milk and 3 water..
When you remove 3 litre more , milk proportion is 3*27/30=27/10
So milk left = 27-27/10=243/10
Remaining is water = 30-243/10=57/10
Ratio M:W=(243/10):(57/10)=243:57=81:19

B

But if the question meant repeated two times MORE then do it once more
Proportion of milk in the third change = 3*243/300=243/100
Milk left = 243/10-243/100=(2430-243)/100=2187/100
Water = 30-2187/100=813/100
Ratio = 2187:813=729:271

C

Formula
Final proportion= [1 - (y/x)]^n
= [1- (3/30)]^3
= (9/10)^3=729/1000
Water proportion = 1-729/1000=271/1000
Relative ratio = 729/271

Here,
x = Initial quantity of milk.
y = Replaced water per process.
n = No. of process repeated.
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Posts: 225
Re: 3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

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04 Sep 2018, 02:47
chetan2u wrote:
pratik2018 wrote:
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?
$$a. \frac{2187}{100}$$
$$b. \frac{81}{19}$$
$$c. \frac{729}{271}$$
$$d. \frac{743}{229}$$
$$e. \frac{813}{19}$$

Although there is a formula but this can be calculated easily ..
After first change 27 milk and 3 water..
When you remove 3 litre more , milk proportion is 3*27/30=27/10
So milk left = 27-27/10=243/10
Remaining is water = 30-243/10=57/10
Ratio M:W=(243/10):(57/10)=243:57=81:19

B

Can you tell me where I'm going wrong?
Using formula, the final conc of milk is (27/30)^2
The oa says its c...

Posted from my mobile device
Math Expert
Joined: 02 Aug 2009
Posts: 7986
Re: 3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

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04 Sep 2018, 03:12
rahulkashyap wrote:
chetan2u wrote:
pratik2018 wrote:
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?
$$a. \frac{2187}{100}$$
$$b. \frac{81}{19}$$
$$c. \frac{729}{271}$$
$$d. \frac{743}{229}$$
$$e. \frac{813}{19}$$

Although there is a formula but this can be calculated easily ..
After first change 27 milk and 3 water..
When you remove 3 litre more , milk proportion is 3*27/30=27/10
So milk left = 27-27/10=243/10
Remaining is water = 30-243/10=57/10
Ratio M:W=(243/10):(57/10)=243:57=81:19

B

Can you tell me where I'm going wrong?
Using formula, the final conc of milk is (27/30)^2
The oa says its c...

Posted from my mobile device

Yes this is the straight formula..
The question means repeats 2 times more so total three times..
Quantity of milk = $$(\frac{27}{30})^3=(9/10)^3=729/1000$$
So water = 1-729/1000=271/1000

Ratio M:W= 729:271
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Re: 3L of milk are drawn from a container containing 30L of milk. It is re   [#permalink] 04 Sep 2018, 03:12
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