NEW HERE? LEARN MORE
closeclose
Last visit was: 28 Apr 2024, 00:22 It is currently 28 Apr 2024, 00:22
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

A vessel (capacity 10 liters) is filled entirely with petrol and keros

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92959
Own Kudos [?]: 619546 [11]
Given Kudos: 81611
Send PM
CAT Tests Forum Quiz Mode
A vessel (capacity 10 liters) is filled entirely with petrol and keros [#permalink] New post   28 Dec 2021, 05:45
11
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

65% (02:43) correct 35% (02:33) wrong based on 78 sessions
Hide Show timer Statistics
A vessel (capacity 10 liters) is filled entirely with petrol and kerosene in the ratio 3:2. Two liters of this solution is removed and replaced with 2 ltrs of kerosene. This procedure is repeated thrice. Find the % of petrol in the resulting solution.

(A) 20%
(B) 30.72%
(C) 40.23%
(D) 52.15%
(E) 63.2%


Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
B
User avatar
B
Himanshiog
Intern
Intern
Joined: 20 Jul 2021
Posts: 15
Own Kudos [?]: 4 [0]
Given Kudos: 64
Location: India
Send PM
Re: A vessel (capacity 10 liters) is filled entirely with petrol and keros [#permalink] New post   14 Jan 2023, 03:30
Can some one please solve this question

Posted from my mobile device
User avatar
G
SaquibHGMATWhiz
GMATWhiz Representative
Joined: 23 May 2022
Posts: 640
Own Kudos [?]: 430 [2]
Given Kudos: 6
Location: India
GMAT 1: 760 Q51 V40
Send PM
A vessel (capacity 10 liters) is filled entirely with petrol and keros [#permalink] New post   Updated on: 26 Mar 2023, 11:21
2
Kudos
Expert Reply
Bunuel wrote:
A vessel (capacity 10 liters) is filled entirely with petrol and kerosene in the ratio 3:2. Two liters of this solution is removed and replaced with 2 ltrs of kerosene. This procedure is repeated thrice. Find the % of petrol in the resulting solution.

(A) 20%
(B) 30.72%
(C) 40.23%
(D) 52.15%
(E) 63.2%


Solution:

  • Capactity of vessel \(= 10\) liters
  • Inital amount of petrol \(=\frac{3}{2+3}\times 10=\frac{3}{5}\times 10=6\) liters
  • Inital amount of kerosene \(=\frac{2}{2+3}\times 10=\frac{2}{5}\times 10=4\) liters

  • Every time, \(\frac{2}{10}\) of the solution gets eliminated
  • So, after 3 removal volume of petrol will be \(=6(1-\frac{2}{10})^3\)
    \(=6(\frac{8}{10})^3\)
    \(=6(\frac{4}{5})^3\)
    \(=6\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\)
    \(=3.072\)
  • Percentage in the final solution \(=\frac{3.072}{10}\times 100=30.72\%\)

Hence the right answer is Option B

Originally posted by SaquibHGMATWhiz on 14 Jan 2023, 05:26.
Last edited by SaquibHGMATWhiz on 26 Mar 2023, 11:21, edited 1 time in total.
User avatar
B
VoxNihili
Intern
Intern
Joined: 29 Dec 2022
Posts: 13
Own Kudos [?]: 7 [1]
Given Kudos: 7
Location: United States
Send PM
A vessel (capacity 10 liters) is filled entirely with petrol and keros [#permalink] New post   14 Jan 2023, 07:04
1
Kudos
SaquibHGMATWhiz wrote:
Bunuel wrote:
A vessel (capacity 10 liters) is filled entirely with petrol and kerosene in the ratio 3:2. Two liters of this solution is removed and replaced with 2 ltrs of kerosene. This procedure is repeated thrice. Find the % of petrol in the resulting solution.

(A) 20%
(B) 30.72%
(C) 40.23%
(D) 52.15%
(E) 63.2%


Solution:

  • Capactity of vessel \(= 10\) liters
  • Inital amount of petrol \(=\frac{3}{2+3}\times 10=\frac{3}{5}\times 10=6\) liters
  • Inital amount of kerosene \(=\frac{2}{2+3}\times 10=\frac{2}{5}\times 10=4\) liters

  • Every time, \(\frac{2}{10}\) of the petrol gets eliminated
  • So, after 3 removal volume of petrol will be \(=6(1-\frac{2}{10})^3\)
    \(=6(\frac{8}{10})^3\)
    \(=6(\frac{4}{5})^3\)
    \(=6\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\)
    \(=3.072\)
  • Percentage in the final solution \(=\frac{3.072}{10}\times 100=30.72\%\)

Hence the right answer is Option B


Hi SaquibHGMATWhiz - I couldn't catch the below part quite well. Can you please let me know how did we conclude that

Quote:
Every time, \(\frac{2}{10}\) of the petrol gets eliminated


Thanks in advance
User avatar
B
ChanSu
Intern
Intern
Joined: 22 Feb 2020
Posts: 18
Own Kudos [?]: 5 [0]
Given Kudos: 32
Send PM
Re: A vessel (capacity 10 liters) is filled entirely with petrol and keros [#permalink] New post   14 Jan 2023, 08:29
SaquibHGMATWhiz wrote:
Bunuel wrote:
A vessel (capacity 10 liters) is filled entirely with petrol and kerosene in the ratio 3:2. Two liters of this solution is removed and replaced with 2 ltrs of kerosene. This procedure is repeated thrice. Find the % of petrol in the resulting solution.

(A) 20%
(B) 30.72%
(C) 40.23%
(D) 52.15%
(E) 63.2%


Solution:

  • Capactity of vessel \(= 10\) liters
  • Inital amount of petrol \(=\frac{3}{2+3}\times 10=\frac{3}{5}\times 10=6\) liters
  • Inital amount of kerosene \(=\frac{2}{2+3}\times 10=\frac{2}{5}\times 10=4\) liters

  • Every time, \(\frac{2}{10}\) of the petrol gets eliminated
  • So, after 3 removal volume of petrol will be \(=6(1-\frac{2}{10})^3\)
    \(=6(\frac{8}{10})^3\)
    \(=6(\frac{4}{5})^3\)
    \(=6\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\)
    \(=3.072\)
  • Percentage in the final solution \(=\frac{3.072}{10}\times 100=30.72\%\)

Hence the right answer is Option B

I thought the question stem said 2 liters of “solution” gets removed (not just “petrol”).

Posted from my mobile device
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8021
Own Kudos [?]: 4100 [2]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User CAT Tests
Re: A vessel (capacity 10 liters) is filled entirely with petrol and keros [#permalink] New post   15 Jan 2023, 02:14
2
Kudos
for this replacement questions use following
( 1- x/10)^n
x is qty of replacement and n is number of times replacement is being done
in this case x is 2 and n is 3
we get ( 1-2/10)^3
(8/10)^3
qty of petrol 6 and that of kerosene 4
% of petrol left will be
6 * ( .8)^3 /100
30.72%


Bunuel wrote:
A vessel (capacity 10 liters) is filled entirely with petrol and kerosene in the ratio 3:2. Two liters of this solution is removed and replaced with 2 ltrs of kerosene. This procedure is repeated thrice. Find the % of petrol in the resulting solution.

(A) 20%
(B) 30.72%
(C) 40.23%
(D) 52.15%
(E) 63.2%


Are You Up For the Challenge: 700 Level Questions
User avatar
B
prachisaraf
Intern
Intern
Joined: 03 Jan 2023
Posts: 30
Own Kudos [?]: 4 [0]
Given Kudos: 300
Send PM
Re: A vessel (capacity 10 liters) is filled entirely with petrol and keros [#permalink] New post   26 Mar 2023, 10:11
ChanSu wrote:
SaquibHGMATWhiz wrote:
Bunuel wrote:
A vessel (capacity 10 liters) is filled entirely with petrol and kerosene in the ratio 3:2. Two liters of this solution is removed and replaced with 2 ltrs of kerosene. This procedure is repeated thrice. Find the % of petrol in the resulting solution.

(A) 20%
(B) 30.72%
(C) 40.23%
(D) 52.15%
(E) 63.2%


Solution:

  • Capactity of vessel \(= 10\) liters
  • Inital amount of petrol \(=\frac{3}{2+3}\times 10=\frac{3}{5}\times 10=6\) liters
  • Inital amount of kerosene \(=\frac{2}{2+3}\times 10=\frac{2}{5}\times 10=4\) liters

  • Every time, \(\frac{2}{10}\) of the petrol gets eliminated
  • So, after 3 removal volume of petrol will be \(=6(1-\frac{2}{10})^3\)
    \(=6(\frac{8}{10})^3\)
    \(=6(\frac{4}{5})^3\)
    \(=6\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\)
    \(=3.072\)
  • Percentage in the final solution \(=\frac{3.072}{10}\times 100=30.72\%\)

Hence the right answer is Option B

I thought the question stem said 2 liters of “solution” gets removed (not just “petrol”).

Same doubt.
User avatar
G
SaquibHGMATWhiz
GMATWhiz Representative
Joined: 23 May 2022
Posts: 640
Own Kudos [?]: 430 [2]
Given Kudos: 6
Location: India
GMAT 1: 760 Q51 V40
Send PM
A vessel (capacity 10 liters) is filled entirely with petrol and keros [#permalink] New post   26 Mar 2023, 11:28
2
Kudos
Expert Reply
ChanSu wrote:
I thought the question stem said 2 liters of “solution” gets removed (not just “petrol”).

Posted from my mobile device


prachisaraf wrote:
I thought the question stem said 2 liters of “solution” gets removed (not just “petrol”).

Same doubt.


Hi Prachi and ChanSu,

That was a typo. I have corrected it now. It is a solution only.

So what happens in such a question can be understood in the following manner.


1. First we have 10 liters of a solution with 6 liters of petrol and remove 2 from it so we have 8 liters of solution left.
    So both petrol and kerosene get reduced to \(\frac{8}{10}\) of the initial amount.
    This means we have 6 × \(\frac{8}{10}\) liter of petrol
    Next, we add kerosene. But it does not change the amount of petrol
2. Now we have 10 liters of solution with 6 × \(\frac{8}{10}\) liters of petrol.
    And we do a similar process as above so our net petrol becomes 6 × \(\frac{8}{10}\) × \(\frac{8}{10}\)

Once we repeat this process again we multiply it again by \(\frac{8}{10}\)

Hope this helps.
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14835
Own Kudos [?]: 64960 [0]
Given Kudos: 428
Location: Pune, India
Send PM
A vessel (capacity 10 liters) is filled entirely with petrol and keros [#permalink] New post   26 Mar 2023, 23:26
Expert Reply
Bunuel wrote:
A vessel (capacity 10 liters) is filled entirely with petrol and kerosene in the ratio 3:2. Two liters of this solution is removed and replaced with 2 ltrs of kerosene. This procedure is repeated thrice. Find the % of petrol in the resulting solution.

(A) 20%
(B) 30.72%
(C) 40.23%
(D) 52.15%
(E) 63.2%


Are You Up For the Challenge: 700 Level Questions


Check out this post first: https://anaprep.com/arithmetic-replacement-in-mixtures/

While working with the ingredient that we are NOT adding back, i.e. petrol here,

\(Cf = Ci * \frac{Vi}{Vf}\)

Vi = Volume after removal
Vf = Volume after replacing back.

Since the process is repeated twice more, we get
\(Cf = Ci * (\frac{Vi}{Vf})^3\)

\(Cf = \frac{3}{5} * (\frac{8}{10})^3 \)

Now, \(\frac{8}{10} = \frac{4}{5}\) and \((\frac{4}{5})^3 = \frac{64}{125}\)

Note that \(\frac{64}{125}\) is slightly more than \(\frac{1}{2}\) because \(\frac{62.5}{125}\) will be exactly half.

So Cf = 60% * slightly more than \(\frac{1}{2}\)

So Cf = Slightly more than 30%

Answer (B)
GMAT Club Bot
gmatclubot
A vessel (capacity 10 liters) is filled entirely with petrol and keros [#permalink]
26 Mar 2023, 23:26
Moderators:
Bunuel
Math Expert
92959 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions