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Two bottles are partially filled with water. The larger bottle current

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Two bottles are partially filled with water. The larger bottle current  [#permalink]

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New post 04 Aug 2016, 11:06
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Question Stats:

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Two bottles are partially filled with water. The larger bottle currently holds \(\frac{1}{3}\) of its capacity. The smaller bottle, which has \(\frac{2}{3}\) of the capacity of the larger bottle, currently holds \(\frac{3}{4}\) of its capacity.If the contents of the smaller bottle are poured into the larger bottle, the larger bottle will be filled to what fraction of its
capacity?

A. \(\frac{5}{6}\)

B. \(\frac{3}{4}\)

C. \(\frac{2}{3}\)

D. \(\frac{7}{12}\)

E. \(\frac{1}{2}\)

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Two bottles are partially filled with water. The larger bottle current  [#permalink]

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New post 04 Aug 2016, 15:13
AbdurRakib wrote:
Two bottles are partially filled with water. The larger bottle currently holds \(\frac{1}{3}\) of its capacity. The smaller bottle, which has \(\frac{2}{3}\) of the capacity of the larger bottle, currently holds \(\frac{3}{4}\) of its capacity.If the contents of the smaller bottle are poured into the larger bottle, the larger bottle will be filled to what fraction of its
capacity?

A. \(\frac{5}{6}\)

B. \(\frac{3}{4}\)

C. \(\frac{2}{3}\)

D. \(\frac{7}{12}\)

E. \(\frac{1}{2}\)


Here the capacity of larger bottle be x and currently the larger bottle has x/3 capacity (given).

Now smaller bottle has 2/3(x) ...( GIVEN: The smaller bottle, which has \(\frac{2}{3}\) of the capacity of the larger bottle )

Currently the SB has 3/4( 2/3(x) ) = 1/2(x) capacity and this is added to larger bottle i.e. 1/2(x) + x/3 = 5/6(x).

Option A is correct answer.
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Re: Two bottles are partially filled with water. The larger bottle current  [#permalink]

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New post 04 Aug 2016, 21:33
AbdurRakib wrote:
Two bottles are partially filled with water. The larger bottle currently holds \(\frac{1}{3}\) of its capacity. The smaller bottle, which has \(\frac{2}{3}\) of the capacity of the larger bottle, currently holds \(\frac{3}{4}\) of its capacity.If the contents of the smaller bottle are poured into the larger bottle, the larger bottle will be filled to what fraction of its
capacity?


Let \(L\) be the capacity of the larger bottle
Let \(l\) be the current capacity of the larger bottle. \(l = \frac{1}{3}L\)
Let \(S\) be the capacity of the smaller bottle. \(S = \frac{2}{3}L\)
Let \(s\) be the current capacity of the smaller bottle. \(s = \frac{3}{4}S\)

Question: What is \(l + s\)

First get \(s\) in terms of \(L\)

\(s = \frac{3}{4} \times \frac{2}{3}L = \frac{1}{2}L\)

\(s + l = (\frac{1}{2} + \frac{1}{3})L = \frac{5}{6}L\)

A. \(\frac{5}{6}\)

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Re: Two bottles are partially filled with water. The larger bottle current  [#permalink]

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New post 12 Aug 2018, 07:18
Let the capacity of larger water bottle be "x"
Water filled in the larger bottle=x/3
Water filled in the smaller bottle=2x/3*3/4=x/2
If we pour the smaller bottle to bigger bottle i.e. x/3+x/2=5x/6=>5/6

Answer(A)
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Re: Two bottles are partially filled with water. The larger bottle current  [#permalink]

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New post 04 Sep 2018, 22:21
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Take larger bottle (L) to have capacity 9 L and since smaller bottle(S) has 2/3rd the larger bottles capacity, S = 6 L capacity.

Now we are told that L is filled up to 1/3rd its capacity i.e 3 L.

S is filled up to 3/4th its capacity i.e 4.5 L.

when we add 4.5 L to 3 L we get 7.5 L.

7.5/9 = 75/90 = 15/18 = 5/6
Hence answer is A.
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Re: Two bottles are partially filled with water. The larger bottle current &nbs [#permalink] 04 Sep 2018, 22:21
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