Last visit was: 21 May 2024, 18:40 It is currently 21 May 2024, 18:40
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# To 100 litres of milk, 10 litres of water is added and then 20 litres

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 93373
Own Kudos [?]: 625648 [49]
Given Kudos: 81918
Tutor
Joined: 16 Oct 2010
Posts: 14891
Own Kudos [?]: 65407 [17]
Given Kudos: 431
Location: Pune, India
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18886
Own Kudos [?]: 22291 [12]
Given Kudos: 285
Location: United States (CA)
General Discussion
Director
Joined: 25 Jul 2018
Posts: 667
Own Kudos [?]: 1120 [3]
Given Kudos: 69
To 100 litres of milk, 10 litres of water is added and then 20 litres [#permalink]
3
Bookmarks
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

Posted from my mobile device
Intern
Joined: 16 Oct 2018
Posts: 32
Own Kudos [?]: 12 [0]
Given Kudos: 17
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?
Intern
Joined: 16 Oct 2018
Posts: 32
Own Kudos [?]: 12 [0]
Given Kudos: 17
Re: To 100 litres of milk, 10 litres of water is added and then 20 litres [#permalink]
Could you help me with the solution using Cf = Ci * (Vi/Vf).
Intern
Joined: 16 Oct 2018
Posts: 32
Own Kudos [?]: 12 [0]
Given Kudos: 17
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
Intern
Joined: 29 May 2017
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 242
Location: United Arab Emirates
GMAT 1: 700 Q54 V58
GPA: 2.86
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?
Tutor
Joined: 16 Oct 2010
Posts: 14891
Own Kudos [?]: 65407 [0]
Given Kudos: 431
Location: Pune, India
Re: To 100 litres of milk, 10 litres of water is added and then 20 litres [#permalink]
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
Current Student
Joined: 27 Jan 2017
Posts: 19
Own Kudos [?]: 13 [1]
Given Kudos: 164
Location: India
GRE 1: Q163 V158
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
Intern
Joined: 25 Jul 2020
Posts: 2
Own Kudos [?]: 1 [1]
Given Kudos: 14
Re: To 100 litres of milk, 10 litres of water is added and then 20 litres [#permalink]
1
Bookmarks
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

Couldn't understand the power i.e. ^n part, can anyone explain?
Director
Joined: 29 Oct 2015
Posts: 730
Own Kudos [?]: 333 [0]
Given Kudos: 476
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