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Bottle X is 2/3 full of water and has half the capacity of Bottle Y.

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Bottle X is 2/3 full of water and has half the capacity of Bottle Y.  [#permalink]

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New post 11 Jan 2018, 23:20
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Bottle X is 2/3 full of water and has half the capacity of Bottle Y. Bottle Y is 1/2 full of water and has twice the capacity of Bottle Z, which is 1/4 full of water. If Bottle X and Bottle Z were poured into Bottle Y, Bottle Y would then be filled to what fraction of capacity?

A. 23/24

B. 11/12

C. 7/8

D. 2/3

E. 1/2

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Re: Bottle X is 2/3 full of water and has half the capacity of Bottle Y.  [#permalink]

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New post 12 Jan 2018, 09:17
According to the capacity ratios, let the cap of bottles X,Y& Z be 12, 24 & 12 litres.
Then vol of water in X, Y & Z is 8L, 12L and 3L.
If X and Z are poured in Y, water in Y would be 23L.
Thus the fraction of water filled= 23/24.
Ans - A, IMO.
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Bottle X is 2/3 full of water and has half the capacity of Bottle Y.  [#permalink]

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New post 12 Jan 2018, 09:38
Bunuel wrote:
Bottle X is 2/3 full of water and has half the capacity of Bottle Y. Bottle Y is 1/2 full of water and has twice the capacity of Bottle Z, which is 1/4 full of water. If Bottle X and Bottle Z were poured into Bottle Y, Bottle Y would then be filled to what fraction of capacity?

A. 23/24

B. 11/12

C. 7/8

D. 2/3

E. 1/2

This question is not hard, but the language is tricky. Assigning values is efficient.

Break the setup (and hence the language) into two parts: capacity, then actual amount of water in each.

Use the LCM of the denominators for the biggest number: 2*3*4 = 24

Capacity
X has \(\frac{1}{2}\) of Y's capacity
Y has twice Z's capacity
Y is the largest
X and Z have equal capacity
Let Y = 24
Let X = 12
Let Z = 12

Amount of water in each bottle
(fraction full)*(capacity) = amount of water
Y is \(\frac{1}{2}\) full: \(\frac{1}{2}\) * 24 = 12 units of water in Y

X is \(\frac{2}{3}\) full: \(\frac{2}{3}\) * 12 = 8 units of water in X

Z is \(\frac{1}{4}\) full: \(\frac{1}{4}\) * 12 = 3 units of water in Z

Bottle Y is filled to what fraction of its capacity?
All the water in X and Z is poured into Y
X + Z: (8 + 3) = 11 units
Y has 12 units
Y has (11 + 12) = 23 units of water in it

Bottle Y is filled to what fraction of capacity?

\(\frac{Part}{Whole}=\frac{AmtOfWater}{Capacity}=\frac{23}{24}\)

Answer A

Algebraically
Define X and Z in terms of Y.
Water in X: \(\frac{1}{2}Y * \frac{2}{3}=\frac{1}{3}Y\)

Water in Z: \(\frac{1}{2}Y*\frac{1}{4}=\frac{1}{8}Y\)

Water in Y: \(\frac{1}{2}Y\)

Bottle Y is filled to what capacity?

\(\frac{1}{3}Y +
\frac{1}{8}Y +\frac{1}{2}Y =\)

\((\frac{8}{24}Y +\frac{3}{24}Y+\frac{12}{24}Y) = \frac{23}{24}
Y\)

Answer A
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Bottle X is 2/3 full of water and has half the capacity of Bottle Y. &nbs [#permalink] 12 Jan 2018, 09:38
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