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

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

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New post Updated on: 31 Jul 2019, 08:26
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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, 08:08.
Last edited by Bunuel on 31 Jul 2019, 08:26, 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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New post 01 Aug 2019, 08:25
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
VeritasKarishma could you please help in solving this mixture conc. based question..
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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New post 04 Aug 2019, 15:59
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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New post 06 Aug 2019, 08:24
Kindly submit solution

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

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New post 06 Aug 2019, 23:42
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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New post 07 Aug 2019, 02:24
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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

Answer (B)

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, 02:24
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