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A bottle is 80% full. The liquid in the bottle consists of 60% guava

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A bottle is 80% full. The liquid in the bottle consists of 60% guava [#permalink]

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New post Updated on: 26 Jun 2017, 08:12
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A bottle is 80% full. The liquid in the bottle consists of 60% guava juice and 40% pineapple juice. The remainder of the bottle is then filled with 70 mL of rum. How much guava juice is in the bottle?

A. 168 mL
B. 170 mL
C. 200 mL
D. 210 mL
E. 250 mL


enigma123: Here is the solution.

We know that the bottle is 80% full. This means that it is 20% empty. This 20% is filled up when you put 70 ml of rum. Since 20% of the bottle is 70 ml, 80% (i.e. 4 times), will be 280 ml (4 times).

So the total volume of the liquid in the bottle is 280 ml. 60% of this 280 ml is guava juice and 40% is pineapple juice.
60% of 280 = 168ml

In % questions, focus on the base i.e. 60% of what? Is it 60% of the bottle or is it 60% of the liquid.

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Originally posted by VeritasPrepKarishma on 11 Jul 2011, 04:37.
Last edited by Bunuel on 26 Jun 2017, 08:12, edited 1 time in total.
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Re: A bottle is 80% full. The liquid in the bottle consists of 60% guava [#permalink]

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New post 08 Dec 2011, 07:18
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A bottle is 80% full. The liquid in the bottle consists of 60% guava juice and 40% pineapple juice. The remainder of the bottle is then filled with 70 lm of rum. How much guava is in the bottle?

OA:
168 ml


Here is how I approached it:
since 80% filled, then 20%of x= 70lm

so x, the capacity, = 70/ .2= 350 lm, the total capacity of the bottle

since 60% of the liquid is guava juice, then .6(350)=210 lm

hence, 210 is the guava juice in the bottle and this is the answer that i got.

but the answer in the book is 168 lm, so can someone please tell me what's the problem with my approach?

please, help
thank you so much

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Re: A bottle is 80% full. The liquid in the bottle consists of 60% guava [#permalink]

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New post 08 Dec 2011, 08:02
1
if the Bottle is 100 ml:
we have 48% Guava, 32% Pineapple, and 20% Rum.
Now, is the bottle 20% of rum is represented by 70 ml. So, we have to find for the same bottle 48% guava is what ml?
therefore, Guava= (70*48)/20= 168 ml
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Re: A bottle is 80% full. The liquid in the bottle consists of 60% guava [#permalink]

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New post 08 Dec 2011, 08:49
manalq8 wrote:
Hi everyone,

I can't figure out what wrong did I do. here is the problem:

A bottle is 80% full. the liquid in the bottle consists of 60% guava juice and 40% pineapple juice. the remainder of the bottle is then filled with 70 lm of rum. How much guava is in the bottle?


here is how I approached it:

since 80% filled, then 20%of x= 70lm

so x, the capacity, = 70/ .2= 350 lm, the total capacity of the bottle

since 60% of the liquid is guava juice, then .6(350)=210 lm

hence, 210 is the guava juice in the bottle and this is the answer that i got.

but the answer in the book is 168 lm, so can someone please tell me what's the problem with my approach?

please, help
thank you so much


Everything you have done so far is correct. 210 is a trap answer, however.

Since the bottle is only 80% filled with the mixture of guava and pineapple, the solution gets diluted when the rum is added.

So going from where you left off that 60% of liquid is guava yielding 210lm:

210lm * 80% of total = 168lm.

The 210lm would be accurate if the bottle was filled with the same ratio of pineapple to guava for the last 80%. However, rum is used instead, so you must account for the new material that makes up 20% of the bottle.

BDSunDevil's method also works, but I found this one to be more intuitive (for me, at least). Hope this helped.
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Re: A bottle is 80% full. The liquid in the bottle consists of 60% guava [#permalink]

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New post 08 Dec 2011, 09:33
Bottle has 80% juice of which 60% is guava
guava juice is 48 % of bottle...... since rum( 20%) is 70ml.......then guava juice is 70*2.4 = 168ml
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Re: A bottle is 80% full. The liquid in the bottle consists of 60% guava [#permalink]

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New post 08 Dec 2011, 15:13
avenkatesh007,
why did you multiply 70 by 2.4? and why originally did u multiply the 70? :(
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Re: A bottle is 80% full. The liquid in the bottle consists of 60% guava [#permalink]

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New post 09 Dec 2011, 03:06
manalq8 wrote:
Hi everyone,

I can't figure out what wrong did I do. here is the problem:

A bottle is 80% full. the liquid in the bottle consists of 60% guava juice and 40% pineapple juice. the remainder of the bottle is then filled with 70 lm of rum. How much guava is in the bottle?


here is how I approached it:

since 80% filled, then 20%of x= 70lm

so x, the capacity, = 70/ .2= 350 lm, the total capacity of the bottle

since 60% of the liquid is guava juice, then .6(350)=210 lm

hence, 210 is the guava juice in the bottle and this is the answer that i got.

but the answer in the book is 168 lm, so can someone please tell me what's the problem with my approach?

please, help
thank you so much


The question tells you the following:
A bottle is 80% full of a liquid. [highlight]60% of the liquid[/highlight] is guava juice and [highlight]40% of the liquid[/highlight] is pineapple juice. (mind you, this is not 60% of the bottle. Say, if the bottle's volume is 100 ml, liquid in it is 80 ml. Guava juice is 60% of the 80 ml (= 48 ml), not of the 100 ml. Similarly, pineapple juice is 40% of the 80 ml (= 32 ml) )

So what [highlight]% of the bottle[/highlight] is full of guava juice? 60% of the 80% = 48%
What [highlight]% of the bottle[/highlight] is full of pineapple juice? 40% of the 80% = 32%
Total 48%+32% = 80% as expected since the total liquid in the bottle is 80%

Rum = 20% of the bottle which is 70 ml
Total volume of the bottle = 350 ml
Guava juice is 48% of the bottle = 48% of 350 = 168 ml
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Re: A bottle is 80% full. The liquid in the bottle consists of 60% guava [#permalink]

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New post 09 Dec 2011, 03:08
manalq8 wrote:
Hi everyone,

I can't figure out what wrong did I do. here is the problem:

A bottle is 80% full. the liquid in the bottle consists of 60% guava juice and 40% pineapple juice. the remainder of the bottle is then filled with 70 lm of rum. How much guava is in the bottle?


here is how I approached it:

since 80% filled, then 20%of x= 70lm

so x, the capacity, = 70/ .2= 350 lm, the total capacity of the bottle

since 60% of the liquid is guava juice, then .6(350)=210 lm

hence, 210 is the guava juice in the bottle and this is the answer that i got.

but the answer in the book is 168 lm, so can someone please tell me what's the problem with my approach?

please, help
thank you so much


Therefore, when you say, "60% of the liquid is guava juice, then .6(350)=210 lm", you make an error. It is not 60% of 350 because that is the volume of the bottle. It is 60% of 80% of 350 = .6 * .8 * 350 = 168 ml
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Re: A bottle is 80% full. The liquid in the bottle consists of 60% guava [#permalink]

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New post 08 Jul 2016, 02:05
manalq8 wrote:
A bottle is 80% full. The liquid in the bottle consists of 60% guava juice and 40% pineapple juice. The remainder of the bottle is then filled with 70 lm of rum. How much guava is in the bottle?



Assume the total volume = 100x
Volume of liquid in the bottle = 80x

Guava juice = 0.6*80x = 48x
Pineapple juice = 0.4*80x = 32x

Remainder of bottle = 20x = 70 ml
x = 3.5ml

Hence, guava juice = 48*3.5 = 168 ml
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Re: A bottle is 80% full. The liquid in the bottle consists of 60% guava [#permalink]

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New post 08 Jul 2016, 05:23
manalq8 wrote:
A bottle is 80% full. The liquid in the bottle consists of 60% guava juice and 40% pineapple juice. The remainder of the bottle is then filled with 70 lm of rum. How much guava is in the bottle?

OA:
168 ml




Here is how I did it.

If 20% is 70ml, 80%= 70* 80/20= 280

Out of this 80%, 60% is guava

280/860/100= 168
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Re: A bottle is 80% full. The liquid in the bottle consists of 60% guava [#permalink]

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New post 20 Jul 2016, 05:18
bottle is 80% full = 0.8x (where x is the total capacity of the bottle)
The liquid in the bottle consists of 60% guava juice = 0.8x*0.6=0.48x
40% pineapple juice = 0.8x*0.4=0.32x

as per the question

0.2x=70
x= 350
guava juice = 0.48*350=168 ml
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Re: A bottle is 80% full. The liquid in the bottle consists of 60% guava [#permalink]

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New post 12 Nov 2016, 14:57
Here is my approach.
We can actually solve this via different methods
Lets use the percent approach.
20 percent => 70 ml
hence 100 percent => 350 ml

80 percent => 280 ml
so out of 280 ml => 60 percent is guava juice.
60/100 *280 => 168.
so currently there is 168 ml of Guava Juice.
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Re: A bottle is 80% full. The liquid in the bottle consists of 60% guava [#permalink]

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New post 26 Jun 2017, 13:17
A bottle is 80% full. The liquid in the bottle consists of 60% guava juice and 40% pineapple juice. The remainder of the bottle is then filled with 70 mL of rum. How much guava juice is in the bottle?

Bottle is 80% Full

Remaining portion is 70mL rum

Which means 20% = 70mL

So, we can calculate, the volume of 80% = \(\frac{80 * 70}{20}\)

So, 80% volume \(= 280 mL\)

Guava is 60% of 280 mL

\(= \frac{60 * 280}{100}\)

= 168 mL

Hence, the answer is A
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Re: A bottle is 80% full. The liquid in the bottle consists of 60% guava [#permalink]

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New post 28 Jun 2017, 16:55
VeritasPrepKarishma wrote:
A bottle is 80% full. The liquid in the bottle consists of 60% guava juice and 40% pineapple juice. The remainder of the bottle is then filled with 70 mL of rum. How much guava juice is in the bottle?

A. 168 mL
B. 170 mL
C. 200 mL
D. 210 mL
E. 250 mL


Since the bottle is initially 80% full and the remainder of the bottle is filled with 70 mL of rum, the amount of rum accounts for 20% of the capacity of the bottle. We can let x = the total number of mLs in the bottle and create the following equation:

0.2x = 70

x = 70/0.2

x = 350

The capacity of the entire bottle is 350 mL. This means that it was initially filled with 80% of 350 mL of juice, which is 0.8 x 350 = 280.

So, the bottle initially had 280 mL of juice and 60% of that amount was guava juice: 0.6 x 280 = 168 mL.

Answer: A
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Re: A bottle is 80% full. The liquid in the bottle consists of 60% guava [#permalink]

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New post 13 Jan 2018, 10:42
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VeritasPrepKarishma wrote:
A bottle is 80% full. The liquid in the bottle consists of 60% guava juice and 40% pineapple juice. The remainder of the bottle is then filled with 70 mL of rum. How much guava juice is in the bottle?

A. 168 mL
B. 170 mL
C. 200 mL
D. 210 mL
E. 250 mL


The bottle is filled 80% to capacity, and then 70ml of rum makes the bottle 100% filled to capacity.
So, 70ml represents 20% of the capacity.

So, BEFORE the rum was added, there were 280ml of liquid in the bottle (i.e., if 70ml represents 20% of capacity, then 280ml represents 80% of capacity)

We're told that 60% of the liquid is guava juice.
60% of 280ml = 168 ml

Answer: B

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Re: A bottle is 80% full. The liquid in the bottle consists of 60% guava [#permalink]

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New post 13 Jan 2018, 15:17
VeritasPrepKarishma wrote:
A bottle is 80% full. The liquid in the bottle consists of 60% guava juice and 40% pineapple juice. The remainder of the bottle is then filled with 70 mL of rum. How much guava juice is in the bottle?

A. 168 mL
B. 170 mL
C. 200 mL
D. 210 mL
E. 250 mL


.6*.8*(70/.2)=168 mL
A
Re: A bottle is 80% full. The liquid in the bottle consists of 60% guava   [#permalink] 13 Jan 2018, 15:17
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