a PS from Gmat

Question

15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container?

A:45
B:25
C:37.5
D:36
E:42

to be honest, i dont understand this question much, it says 15lts moved out from a container in which there are A and B or 15 lts are taking out from A?

shankar.ashwin · Answer

I posted a solution earlier https://www.beatthegmat.com/container-t92063.html

vaibhavgupta · Answer

diebeatsthegmat wrote:15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container?

A:45
B:25
C:37.5
D:36
E:42

to be honest, i dont understand this question much, it says 15lts moved out from a container in which there are A and B or 15 lts are taking out from A?

IMO C

OA?

If OA is A, IMO B
If OA is B, IMO C
If OA is C, IMO D
If OA is D, IMO E
If OA is E, IMO A

FML!! :/

GMATGuruNY · Answer

diebeatsthegmat wrote:15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container?

A:45
B:25
C:37.5
D:36
E:42

We could also use the formula for REPEATED FRACTIONAL CHANGE.
If amount x DECREASES by fraction a/b exactly n times:

Final amount = x * (1 - a/b)^n.

In the problem at hand (as noted in my post above):
The original amount of A = x.
The final amount = (9/25)x.
The fractional decrease = 15/x.
Since the volume decreases TWICE, n = 2.
Plugging these values into the formula, we get:

(9/25)x = x * (1 - 15/x)²

9/25 = (1 - 15/x)²

3/5 = 1 - 15/x

15/x = 2/5

2x = 75

x = 37.5.

Note that if amount x INCREASES by fraction a/b exactly n times, the formula is as follows:
Final amount = x * (1 + a/b)^n.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

subhakam · Answer

GMATGuruNY wrote:diebeatsthegmat wrote:15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container? A:45 B:25 C:37.5 D:36 E:42 to be honest, i dont understand this question much, it says 15lts moved out from a container in which there are A and B or 15 lts are taking out from A? We can plug in the answers, which represent the volume of the container. Answer choice C: 37.5 liters. After the first mixing, the amount of A remaining in the container = 37.5 - 15 = 22.5 liters. 15 liters of the resulting solution are to be replaced with pure B. Since 15/37.5 = 40%, the second mixing will replace 40% of the remaining 22.5 liters of A. Thus, the amount of A left after the second mixing = .6(22.5) = 13.5 liters. The amount of B after the second mixing = 37.5-13.5 = 24 liters. A:B = 13.5 : 24 = 27:48 = 9:16. Success! The correct answer is C. Sorry GMAT Guru - I still do not get it Can you show it algebraically? I really get confused on the second mixing. if I make a column below and try to track the amount of both A and B - how do i do it ? A B 37.5 0 First take out - 15 liters 37.5-15 +15 = 22.5 15 Can you explain what happens after another 15 are removed - what i get confused about is not only A being reduced but B is being reduced as well (when 15 is being removed the 2nd time) Thanks

GMATGuruNY · Answer

subhakam wrote:GMATGuruNY wrote:diebeatsthegmat wrote:15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container? A:45 B:25 C:37.5 D:36 E:42 Sorry GMAT Guru - I still do not get it Can you show it algebraically? I really get confused on the second mixing. Let the capacity of the container = x. Every time 15 liters are removed, the volume of liquid inside the container decreases by 15/x. To illustrate: If x=30, removing 15 liters from the container -- 1/2 of the volume -- is equivalent to reducing the volume by 15/x = 15/30 = 1/2. If x=45, removing 15 liters from the container -- 1/3 of the volume -- is equivalent to reducing the volume by 15/x = 15/45 = 1/3. Thus, every time 15 liters are removed, the volume of A inside the container decreases by 15/x. At the start, the container is full of A. Thus, the original amount of A = x. When 15 liters are removed, the decrease in A = (15/x)x = 15. Remaining amount of A = x-15. When 15 more liters are removed, the decrease in A = (15/x)(x-15). Remaining amount of A = (x-15) - (15/x)(x-15) = (x-15)*(1 - 15/x) = (x-15)*(x-15)/x. At the end of the process, A:B = 9:16. Since 9+16 = 25, liquid A constitutes 9 of every 25 liters inside the container, implying that A = (9/25)x. Since both expressions in red above represent the amount of A at the end of the process, we get: (x-15)*(x-15)/x = (9/25)x (x-15)² = (9/25)x² x-15 = (3/5)x 5x - 75 = 3x 2x = 75 x = 37.5.

GMATGuruNY · Answer

diebeatsthegmat wrote:15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container?

A:45
B:25
C:37.5
D:36
E:42

We could also use the formula for REPEATED FRACTIONAL CHANGE.
If amount x DECREASES by fraction a/b exactly n times:

Final amount = x * (1 - a/b)^n.

In the problem at hand (as noted in my post above):
The original amount of A = x.
The final amount = (9/25)x.
The fractional decrease = 15/x.
Since the volume decreases TWICE, n = 2.
Plugging these values into the formula, we get:

(9/25)x = x * (1 - 15/x)²

9/25 = (1 - 15/x)²

3/5 = 1 - 15/x

15/x = 2/5

2x = 75

x = 37.5.

Note that if amount x INCREASES by fraction a/b exactly n times, the formula is as follows:
Final amount = x * (1 + a/b)^n.

subhakam · Answer

Thank you so much!! It finally makes sense- come to think of it; we deal with such problems in daily life but never come to stop and think how actually it formulates. Thank you once again for the clarification!!

One quick question - the formula that you posted on your second posting - it is only valid if the same quantity is removed/added repeatedly correct? So, for example we could not have used the direct formula if instead of 15 , 10 liters wee taken out.
Final amount = x * (1 - a/b)^n.
All help greatly appreciated

GMATGuruNY · Answer

subhakam wrote:Thank you so much!! It finally makes sense- come to think of it; we deal with such problems in daily life but never come to stop and think how actually it formulates. Thank you once again for the clarification!!

One quick question - the formula that you posted on your second posting - it is only valid if the same quantity is removed/added repeatedly correct? So, for example we could not have used the direct formula if instead of 15 , 10 liters wee taken out.
Final amount = x * (1 - a/b)^n.
All help greatly appreciated

Correct: the fractional change -- (amount removed)/(total volume) -- must be the same in each case.

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

a PS from Gmat

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER