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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 06 Sep 2019, 01:01
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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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Re: Two bottles are partially filled with water. The larger bottle current  [#permalink]

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New post 06 Sep 2019, 01:44
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Larger bottle is 1/3 full.
Smaller bottle when full is 2/3 the capacity of larger bottle.
We are told that the smaller bottle is 3/4 full.
3/4 of 2/3 = 3/4 *2/3 =1/2
So emptying the contents (i.e. 2/3) of the smaller bottle into bigger bottle is same as adding half of the full capacity of the big bottle.
Hence the larger bottle is now 1/2+1/3 = 5/6 full.
Answer is A.

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

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New post 06 Sep 2019, 01:56
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Given:
1. Two bottles are partially filled with water.
2. The larger bottle currently holds 1/3 of its capacity.
3. The smaller bottle, which has 2/3 of the capacity of the larger bottle, currently holds 3/4 of its capacity.

Asked: 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 the capacity of larger bottle be V
The larger bottle currently holds 1/3 of its capacity. = V/3

The smaller bottle, which has 2/3 of the capacity of the larger bottle = 2V/3
currently holds 3/4 of its capacity. = V/2

If the contents of the smaller bottle are poured into the larger bottle, the larger bottle will be filled = V/3 + V/2 = 5V/6
The larger bottle will be filled to what fraction of its capacity = (5V/6)/V = 5/6

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

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New post 06 Sep 2019, 02:10
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I solved by converting the question in pictorial form. It made the question much more easier to solve!

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

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New post 06 Sep 2019, 02:49
let large be 12 ltrs so its filled to 4 ltrs
and small is 8 ltrs and filled to 6 ltrs
6+4 ; 10 ltrs
10/12 ; 5/6
IMO A:



Two bottles are partially filled with water. The larger bottle currently holds 1/3 of its capacity. The smaller bottle, which has 2/3 of the capacity of the larger bottle, currently holds 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. 5/6

B. 3/4

C. 2/3

D. 7/12
E. 1/2
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Re: Two bottles are partially filled with water. The larger bottle current  [#permalink]

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New post 06 Sep 2019, 02:49
for this questions let us suppose that the larger bottle have the capacity of 30 litters
Larger bottle is filled = 1/3 *30 = 10
smaller bottles have the capacity = 2/3 * 30=20 and it is filled 3/4 of its capacity =10
by the questions if the smaller bottle water is poured to larger bottle the what is the portion of larger bottle is filled with comparison to its capacity
so, portion = larger+smaller/larger full capacity
= 10+10/30
20/30
2/3
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Re: Two bottles are partially filled with water. The larger bottle current  [#permalink]

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New post 06 Sep 2019, 04:27
IMO correct answer is A

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

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New post 06 Sep 2019, 10:54
Capacity of Large bottle = L. Amount of water in large bottle \(= \frac{1}{3}\) L

Capacity of Small bottle = S. Amount of water in small bottle \(= \frac{3}{4} S\). Since \(S = \frac{2}{3}\) L
 Amount of water in small bottle = \(\frac{3}{4} * \frac{2}{3}\) L \(= \frac{1}{2}\) L

Now adding water from small to Large bottle gives = \(\frac{1}{3} + \frac{1}{2}\) L
 \(= \frac{5}{6}\) L

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 06 Sep 2019, 21:02
Let the larger bottle has 120L capacity.
And larger bottle is filled to 1/3 capacity, hence it will have 40L.
Smaller will be 2/3 of 120 = 80L, and it currently holds 3/4 of 80 = 60
so 60+40=100 i.e. 100/120 = 5/6 (A)


Two bottles are partially filled with water. The larger bottle currently holds 1/3 of its capacity. The smaller bottle, which has 2/3 of the capacity of the larger bottle, currently holds 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. 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 06 Sep 2019, 22:37
Consider the capacity is first vessel to be 12 l. And 1/3 of 12= 4 l
As per the statement the capacity of the second container becomes 8 l. And 3/4 of 8= 6 l

Hence, (4+6)/12=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 06 Sep 2019, 22:38
Consider the capacity is first vessel to be 12 l. And 1/3 of 12= 4 l
As per the statement the capacity of the second container becomes 8 l. And 3/4 of 8= 6 l

Hence, (4+6)/12=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 07 Sep 2019, 10:47
If we tAke the capacity of larger bottle to be 12,then it's filled with (1/3)*12=4 . Smaller bottle is filled to(3/4)* (2/3)*12=6

6 is poured into larger bottle,total becomes 10 so, the capacity now is (10/12)=5/6
Option A is the answer
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Re: Two bottles are partially filled with water. The larger bottle current  [#permalink]

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New post 07 Sep 2019, 11:17
Let the capacity of large bottle be x
filled = 1/3x
small bottler capacity in terms of large = 2/3x
filled = 3/4*2/3x
= 1/2x
total water = 1/3x+1/2x
= 5/6x
Ans = A
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Re: Two bottles are partially filled with water. The larger bottle current   [#permalink] 07 Sep 2019, 11:17
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