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Water is poured from a full 5-liter jug into two identical

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Water is poured from a full 5-liter jug into two identical [#permalink]

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15 Feb 2017, 10:06
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Water is poured from a full 5-liter jug into two identical glasses until all three containers are each 3/4 full. What is the capacity, in liters, of one glass?

A) 5/6
B) 8/9
C) 9/8
D) 6/5
E) 5/3

*Kudos for all correct solutions

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Location: India
Concentration: Strategy, General Management
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Water is poured from a full 5-liter jug into two identical [#permalink]

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15 Feb 2017, 10:24
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First jug --> Full quantity = 5

Let x be the quantity of each identical glass.

5 - (3/4)*(2x) = (3/4)*5
20 - 6x = 15
x = 5/6

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Joined: 07 Dec 2014
Posts: 999
Water is poured from a full 5-liter jug into two identical [#permalink]

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15 Feb 2017, 14:49
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GMATPrepNow wrote:
Water is poured from a full 5-liter jug into two identical glasses until all three containers are each 3/4 full. What is the capacity, in liters, of one glass?

A) 5/6
B) 8/9
C) 9/8
D) 6/5
E) 5/3

*Kudos for all correct solutions

1/4*5=5/4 liter
(5/4)/2=5/8 liter
let g=glass capacity
5/8 liter=3/4*g
g=5/6 liter
SVP
Joined: 12 Sep 2015
Posts: 2477
Re: Water is poured from a full 5-liter jug into two identical [#permalink]

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15 Feb 2017, 18:07
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GMATPrepNow wrote:
Water is poured from a full 5-liter jug into two identical glasses until all three containers are each 3/4 full. What is the capacity, in liters, of one glass?

A) 5/6
B) 8/9
C) 9/8
D) 6/5
E) 5/3

Let x = the capacity of each glass (in liters)
So, if the glass is 3/4 full, then (3/4)x = the amount of water in one glass
So, (2)(3/4)x = the amount of water in TWO glasses

IMPORTANT: the volume of water IN the TWO glasses is equal to the volume of water that was poured OUT of the 5-liter jug.
Since the 5-liter jug ends up being 3/4 full, we can conclude that 1/4 of the water was poured OUT of the 5-liter jug.
So, (1/4)(5) = the volume of water that was poured OUT of the 5-liter jug.

Now we'll set up a "word equation"
Volume of water IN the TWO glasses = volume of water poured OUT of the 5-liter jug
We get: (2)(3/4)x = (1/4)(5)
Simplify: 6x/4 = 5/4
Multiply both sides by 4 to get: 6x = 5
Solve: x = 5/6

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Re: Water is poured from a full 5-liter jug into two identical [#permalink]

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15 Feb 2017, 18:15
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GMATPrepNow wrote:
Water is poured from a full 5-liter jug into two identical glasses until all three containers are each 3/4 full. What is the capacity, in liters, of one glass?

A) 5/6
B) 8/9
C) 9/8
D) 6/5
E) 5/3

Another approach:

Since the 5-liter jug ends up being 3/4 full, we can conclude that 1/4 of the water was poured OUT of the 5-liter jug.
1/4 of 5 liters = (1/4)(5) = 5/4 liters

Equal amounts of those 5/4 liters were poured into EACH of the two glasses.
So, (1/2)5/4 liters = volume of water poured into ONE glass
Simplify to get: 5/8 liters = volume of water poured into ONE glass

That volume of 5/8 liters represents 3/4 of the capacity of the glass.
So, if we let c = the capacity of the glass, then 3/4 of c = 5/8 liters
In other words, (3/4)c = 5/8
To solve, multiply both sides by 4/3 to get: c = (4/3)5/8)
= 20/24
= 5/6

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Posts: 1247
Re: Water is poured from a full 5-liter jug into two identical [#permalink]

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15 Feb 2017, 23:00
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Expert's post
GMATPrepNow wrote:
Water is poured from a full 5-liter jug into two identical glasses until all three containers are each 3/4 full. What is the capacity, in liters, of one glass?

A) 5/6
B) 8/9
C) 9/8
D) 6/5
E) 5/3

*Kudos for all correct solutions

• Since all three containers are $$\frac{3}{4}$$th full at the end.

• We can infer that from the jug, we poured $$(1-\frac{3}{4})*5$$ litre in the identical glasses.

• Therefore in each glass, water poured would be $$\frac{1}{2}$$ of $$(1 - \frac{3}{4})*5$$

• If the capacity of the glass is $$G$$, then -
• $$\frac{3}{4} * G =\frac{1}{2} * (1-\frac{3}{4})*5$$

• $$G = \frac{4}{3} *\frac{1}{2} * \frac{1}{4} *5 = \frac{5}{6} litres$$

Hence the correct answer is Option A

Thanks,
Saquib
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Joined: 03 Jan 2017
Posts: 30
Re: Water is poured from a full 5-liter jug into two identical [#permalink]

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17 Feb 2017, 02:47
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(1/4)*5 = (3/4)*2x
X = 5/6.
Option D.....

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Re: Water is poured from a full 5-liter jug into two identical [#permalink]

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19 Mar 2018, 19:45
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Re: Water is poured from a full 5-liter jug into two identical   [#permalink] 19 Mar 2018, 19:45
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