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To 100 litres of milk, 10 litres of water is added and then 20 litres [#permalink]
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100l ( milk) + 10l (water) = 110liters solution
—> \(\frac{100}{110}= \frac{10}{11}\) of 1 liter solution is milk

20 liters solution is removed.
—> \((\frac{10}{11})*20 = (\frac{200}{11})\) liters milk is removed

—> \(100–\frac{200}{11}=( \frac{900}{11})\) liters milk is left.

Then, 90l(solution) + 30l(water) = 120 liters solution
—> from 120 liters solution, 20 liters solution is removed.

In the 120 liters solution:

\(\frac{900}{(11*120)} = \frac{90}{132}\)
—> \(\frac{90}{132}\) of 1 liter solution is milk

\(20*\frac{90}{132}= \frac{1800}{132}= (\frac{150}{11})\)
—> (\(\frac{150}{11}\)) liters of 20 liters solution is milk —> \(\frac{900}{11}\) —\(\frac{150}{11}\)= \(\frac{750}{11}\) liters

—> What is the amount milk in the solution( in liters) ???
\(\frac{750}{11}\) liters milk is left in the solution now

The answer is D

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Re: To 100 litres of milk, 10 litres of water is added and then 20 litres [#permalink]
lacktutor can you or anyone explain how to use the short winded method (cf= ci*vi/vf) to solve this question?
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Re: To 100 litres of milk, 10 litres of water is added and then 20 litres [#permalink]
VeritasKarishma
Could you help me with the solution using Cf = Ci * (Vi/Vf).
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Re: To 100 litres of milk, 10 litres of water is added and then 20 litres [#permalink]
VeritasKarishma Thanks a lot for the reply! That explanation clears the doubt
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Re: To 100 litres of milk, 10 litres of water is added and then 20 litres [#permalink]
VeritasKarishma In the formula you used is Ci (Initial concentration) 100 l of milk ( from the first sentence of the question. just wanted to clarify because you also get 100 when you add and subtract from the solution eventually?
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Re: To 100 litres of milk, 10 litres of water is added and then 20 litres [#permalink]
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nehasiyer wrote:
VeritasKarishma In the formula you used is Ci (Initial concentration) 100 l of milk ( from the first sentence of the question. just wanted to clarify because you also get 100 when you add and subtract from the solution eventually?


Ci = Initial concentration of milk in the solution (so it cannot be 100 lt because that is initial volume of milk)

To 100 lt of milk, 10 lt of water is added. So you get 110 lt of solution.
The concentration of milk in this is 100/110 = 10/11
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Re: To 100 litres of milk, 10 litres of water is added and then 20 litres [#permalink]
Scenario Milk Water Total Calculation using concentration of milk

1 100 0 100
2 100 10 110
100/110 of 1 L thus (100/110)*20 = 200/11 L is removed from milk
, thus 100-(200/11)=900/11 L milk remains when 20Lsolution is removed
3 900/11 90
4 900/11 120 30L water is added
(900/11)/120 of 1 L thus (900/11)/120*20 = 150/11 L is removed from milk
, thus (900/11)-(150/11)=750/11 L milk remains when 20L solution is further removed
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Re: To 100 litres of milk, 10 litres of water is added and then 20 litres [#permalink]
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KarishmaB wrote:
Bunuel wrote:
To 100 litres of milk, 10 litres of water is added and then 20 litres of solution is removed. Next 30 litres of the water is added and 20 litres of solution is removed. What is the amount of milk, in litres, in the solution now?

A. 720/11 litres
B. 730/11 litres
C. 740/11 litres
D. 750/11 litres
E. 760/11 litres


Water is added so we work with the amount of milk. Our iteration begins when we "REMOVE".

We have 100 lts of milk and 10 lts of water so concentration of milk = 10/11 and volume of mix is 110 lts.
We need the final concentration of milk Cf

Cf = Ci *(Vi/Vf)^n

Cf = (10/11) * (90/120) = 30/44 (20 lts is removed and 30 lts added so Vi = 110 - 20 = 90 and Vf = 90 + 30 = 120)

This is the concentration of milk in 120 lts of solution. Now 20 lts is removed with doesn't change the concentration of milk.

Volume of solution after removing 20 lts = 120 - 20 = 100 lts
Amount of milk in it = 100*(30/44) = 750/11 litres

Answer (D)



Couldn't understand the power i.e. ^n part, can anyone explain?
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Re: To 100 litres of milk, 10 litres of water is added and then 20 litres [#permalink]
KarishmaB What is the significance of vi/ vf ? Can you please explain each part of this formulae ? I am not comfortable using this formulae . Please help.
KarishmaB wrote:
Bunuel wrote:
To 100 litres of milk, 10 litres of water is added and then 20 litres of solution is removed. Next 30 litres of the water is added and 20 litres of solution is removed. What is the amount of milk, in litres, in the solution now?

A. 720/11 litres
B. 730/11 litres
C. 740/11 litres
D. 750/11 litres
E. 760/11 litres

Water is added so we work with the amount of milk. Our iteration begins when we "REMOVE".

We have 100 lts of milk and 10 lts of water so concentration of milk = 10/11 and volume of mix is 110 lts.
We need the final concentration of milk Cf

Cf = Ci *(Vi/Vf)^n

Cf = (10/11) * (90/120) = 30/44 (20 lts is removed and 30 lts added so Vi = 110 - 20 = 90 and Vf = 90 + 30 = 120)

This is the concentration of milk in 120 lts of solution. Now 20 lts is removed with doesn't change the concentration of milk.

Volume of solution after removing 20 lts = 120 - 20 = 100 lts
Amount of milk in it = 100*(30/44) = 750/11 litres

Answer (D)

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Re: To 100 litres of milk, 10 litres of water is added and then 20 litres [#permalink]
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