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# Starting from a certain mixture of milk and water, 10% mixture was rem

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Intern
Joined: 23 Jun 2019
Posts: 12
Starting from a certain mixture of milk and water, 10% mixture was rem  [#permalink]

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Updated on: 31 Jul 2019, 07:26
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Difficulty:

85% (hard)

Question Stats:

43% (02:34) correct 57% (02:22) wrong based on 30 sessions

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Starting from a certain mixture of milk and water, 10% mixture was removed and replaced by pure milk. The same process was repeated by successively removing and replacing 20%, 30% and 40% of the mixture with pure milk. If the ratio of milk to water in the final mixture is 68:7 then the initial ratio was

(A) 11:4
(B) 56:25`
(C) 18:7
(D) 16:9
(E) 15:9

Originally posted by Harshita6789 on 31 Jul 2019, 07:08.
Last edited by Bunuel on 31 Jul 2019, 07:26, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Starting from a certain mixture of milk and water, 10% mixture was rem  [#permalink]

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01 Aug 2019, 07:25
Harshita6789 wrote:
Starting from a certain mixture of milk and water, 10% mixture was removed and replaced by pure milk. The same process was repeated by successively removing and replacing 20%, 30% and 40% of the mixture with pure milk. If the ratio of milk to water in the final mixture is 68:7 then the initial ratio was

(A) 11:4
(B) 56:25`
(C) 18:7
(D) 16:9
(E) 15:9

Harshita6789 is the question complete ? initial conc. of milk and water is missing
im not able to figure out how to use formula c2/c1=v1/v2 here...
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Re: Starting from a certain mixture of milk and water, 10% mixture was rem  [#permalink]

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04 Aug 2019, 14:59
This doesn't make sense to me.

How can we solve this without the initial concentrations? Are we to assume 50:50?
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Re: Starting from a certain mixture of milk and water, 10% mixture was rem  [#permalink]

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06 Aug 2019, 07:24
Kindly submit solution

Posted from my mobile device
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Re: Starting from a certain mixture of milk and water, 10% mixture was rem  [#permalink]

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06 Aug 2019, 22:42
Let the total quantity of the mixture be T liters and the initial quantities of water and milk be W and M liters respectively. Let the processes of removing and replenishing be denoted by P1, P2...and so on.

Qty of water after P1 = W - (W/T)*(T/10) = W*(9/10)
Qty of water after P2 = W*(9/10) - {[W*(9/10)]/T}*(2T/10) = W*(9/10)*(8/10)
Qty of water after P3 = W*(9/10)*(8/10)*(7/10)
Qty of water after P4 = W*(9/10)*(8/10)*(7/10)*(6/10)

Since the ratio of water to milk in the final mixture is 7/68, the ratio of water to total qty is 7/(68+7)=7/75.
Therefore, [W*(9/10)*(8/10)*(7/10)*(6/10)]/T = 7/75....> (W/T) = 25/81
Thus, W/M = 25/(81-25)....> W/M = 25/56 ...> M/W = 56/25. ANS : B
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Re: Starting from a certain mixture of milk and water, 10% mixture was rem  [#permalink]

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07 Aug 2019, 01:24
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1
Harshita6789 wrote:
Starting from a certain mixture of milk and water, 10% mixture was removed and replaced by pure milk. The same process was repeated by successively removing and replacing 20%, 30% and 40% of the mixture with pure milk. If the ratio of milk to water in the final mixture is 68:7 then the initial ratio was

(A) 11:4
(B) 56:25`
(C) 18:7
(D) 16:9
(E) 15:9

We are adding back milk so we need to work with water here.
Initial concentration of water = Ci
Final concentration of water = 7/75

7/75 = Ci * (90/100)*(80/100)*(70/100)*(60/100)

Ci = 10*10*10*10/75*9*8*6 = 25/81

Ratio of milk:water initially = 56:25

For more, check: https://www.veritasprep.com/blog/2012/0 ... -mixtures/
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Re: Starting from a certain mixture of milk and water, 10% mixture was rem   [#permalink] 07 Aug 2019, 01:24