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A bowl was half full of water. 4 cups of water were then added to the

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A bowl was half full of water. 4 cups of water were then added to the [#permalink] New post 07 Jul 2011, 21:00
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83% (01:48) correct 17% (00:47) wrong based on 7 sessions
A bowl was half full of water. 4 cups of water were then added to the bowl, filling the bowl to 70% of its capacity. How many cups of water are now in the bowl?

[Reveal] Spoiler: Answer
14

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Re: A bowl was half full of water. 4 cups of water were then added to the [#permalink] New post 07 Jul 2011, 21:18
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enigma123 wrote:
A bowl was half full of water. 4 cups of water were then added to the bowl, filling the bowl to 70% of its capacity. How many cups of water are now in the bowl?

Ans: 14

Can someone on this forum please explain me the concept behind this question i.e. how to approach these questions?
I would like to solve this using the variable i.e. x or something, if you know what I mean. Your help is very much appreciated.


Since you asked for a solution with a variable, Say cup's capacity = x
Bowl's capacity = B
Bowl is half full i.e. 50%B is full
50/100 * B + 4x = 70/100 * B
B = 20x
So Bowl's capacity is of 20 cups. If it is 70% full, it has 70/100 * 20 = 14 cups in it.

Otherwise, just think - Bowl is 50% full. It became 70% full i.e. an increase of 20% by adding 4 cups. So each cup adds 5%. 70% full will have 70/5 = 14 cups.
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Director
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Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
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Location: United Kingdom
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Re: A bowl was half full of water. 4 cups of water were then added to the [#permalink] New post 07 Jul 2011, 21:50
Hi Karishma - Many thanks for a wonderful reply. I understand the 2nd solution. But have a minor doubt in the first solution with variable which I have highlighted:

cup's capacity = x
Bowl's capacity = B
Bowl is half full i.e. 50%B is full
50/100 * B + 4x = 70/100 * B
B = 20x --> How did you get this?
So Bowl's capacity is of 20 cups. If it is 70% full, it has 70/100 * 20 = 14 cups in it.

Apologies if I sound thick and annoying, but your help will be very much appreciated as always.
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MGMAT 1 --> 530
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Re: A bowl was half full of water. 4 cups of water were then added to the [#permalink] New post 07 Jul 2011, 23:39
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enigma123 wrote:
Hi Karishma - Many thanks for a wonderful reply. I understand the 2nd solution. But have a minor doubt in the first solution with variable which I have highlighted:

cup's capacity = x
Bowl's capacity = B
Bowl is half full i.e. 50%B is full
50/100 * B + 4x = 70/100 * B
B = 20x --> How did you get this?
So Bowl's capacity is of 20 cups. If it is 70% full, it has 70/100 * 20 = 14 cups in it.

Apologies if I sound thick and annoying, but your help will be very much appreciated as always.


Np Here it goes

50/100*B+ 4X = 70/100*B
4x = 70/100*B - 50/100*B
4x = 20/100*B

4x*100 = 20*B
400X= 20*B
B = 400/20 *x
B = 20X

hope this helps
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Kudos [?]: 528 [0], given: 217

Re: A bowl was half full of water. 4 cups of water were then added to the [#permalink] New post 08 Jul 2011, 00:02
Thanks Karishma & Sudhir18n. Really appreciate.
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Re: A bowl was half full of water. 4 cups of water were then added to the [#permalink] New post 09 Sep 2011, 12:18
Guess I'm kinda late here, but I'll contribute my 2 cents anyway since I'm this happy with my solution!

The question right away reveals that 20% = 4 cups. Hence 1 cup = 5%.

Therefore, if it was already 50% full, there were 10 cups of water.

Add the 4 cups we just added, that makes it 14.
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Re: A bowl was half full of water. 4 cups of water were then added to the [#permalink] New post 09 Sep 2011, 15:31
lets say total volume of the container = V

Initial water content is half of total volume = V/2

Then 4 cups of water were added.

Current water content = (V/2) + 4 cups = (70/100)V

=> V = 20 cups

=> current water content is equivalent to = V/2+ 4 cups = 20/2 + 4 = 14 cups
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Re: A bowl was half full of water. 4 cups of water were then added to the [#permalink] New post 09 Sep 2011, 16:37
try to translate words. first let denote the capacity as X, so let's start

.5X+4=.7x

now combine like terms
4=.7x-.5x
.2x=4
x=4/.2

multiply each number by 10 to make it easier for you to divide
so , we get
x=40/2

20=x
now, we know that the full capacity is 20 cups
and after adding the 4 cups, the bowl is 70% full so
70% of 20 = 14

hope that helps
dont hesitate if u need any further explination
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Re: A bowl was half full of water. 4 cups of water were then added to the [#permalink] New post 09 Sep 2011, 18:07
4 cup = 20%
hence, 5% = 1 cup i.e. 50% = 10 cup.
Total cup = 10 + 4 = 14 cup
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Re: A bowl was half full of water. 4 cups of water were then added to the [#permalink] New post 10 Sep 2011, 11:52
20% = 4 cups
So 70% = 4/20 * 70 = 14 cups.
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Re: A bowl was half full of water. 4 cups of water were then added to the [#permalink] New post 20 Oct 2014, 07:45
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Re: A bowl was half full of water. 4 cups of water were then added to the   [#permalink] 20 Oct 2014, 07:45
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