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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. \(\frac{1}{2}\)
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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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.
Posted from my mobile device
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
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
