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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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04 Aug 2016, 11:06
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Difficulty:

5% (low)

Question Stats:

85% (01:25) correct 15% (01:31) wrong based on 127 sessions

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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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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).

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

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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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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

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

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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
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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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