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# Two equally sized jugs full of water are each emptied into t

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Two equally sized jugs full of water are each emptied into t [#permalink]

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11 Dec 2012, 07:37
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Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/5 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?

A. 0
B. 1/15
C. 2/15
D. 1/10
E. 2/10

I have tried solving it using no's...Unable to get the right answer.Can anyone elaborate please?
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Re: Two equally sized jugs full of water are each emptied into t [#permalink]

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11 Dec 2012, 09:53
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apoorvarora wrote:
Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/5 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?

a. 0
b. 1/15
c. 2/15
d. 1/10
e. 2/10

I have tried solving it using no's...Unable to get the right answer.Can anyone elaborate please?

Suppose the water in each jug is L liters
CX x (1/5) = L
CX = 5L liters

CX is capacity of X

CY x (2/3) = L
CY = 3L/2 liters

CY is capacity of Y

Now, Y is 3L/2 - L empty = L/2 empty
So, we can put only L/2 water in jug Y from Jug X

Jug X's remaining water = L - L/2 = L/2

Fraction of X which contains water = water / CX
= (L/2)/ 5L
= 1/10

Hope it helps!
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Re: Two equally sized jugs full of water are each emptied into t [#permalink]

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11 Dec 2012, 10:15
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apoorvarora wrote:
Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/5 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?

A. 0
B. 1/15
C. 2/15
D. 1/10
E. 2/10

I have tried solving it using no's...Unable to get the right answer.Can anyone elaborate please?

There are equal amounts of water in jars X and Y, say 2L, then:
The capacity of jar X is 10L (1/5*10=2L).
The capacity of jar Y is 3L (2/3*3=2L).

Now, in order jar Y to be full we need to pour 1L from jar X to jar Y, thus there will be 1L of water left in jar X, which is 1/10 of it.

Similar question to practice: equal-amount-of-water-were-poured-into-two-empty-jars-of-98962.html?hilit=water
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Re: Two equally sized jugs full of water are each emptied into t [#permalink]

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11 Dec 2012, 17:44
thanx...for the explanation

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Re: Two equally sized jugs full of water are each emptied into t [#permalink]

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18 Jun 2013, 01:46
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Jug X is filled 1/5th = 1/5 x.............. (1)
Jug Y is filled 2/3rd = 2/3 y................(2)

From the condition given, (1) = (2)
So, 1/5x = 2/3y.............................. (3)

To fill the Jug Y completely, additional water required-
= y-2/3y
= 1/3y............................................ (4)

Comparing (3) & (4), we get 1/3y = 1/10 x
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Re: Two equally sized jugs full of water are each emptied into t [#permalink]

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02 Apr 2014, 08:08
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$$\frac{1}{5}Cx = \frac{2}{3}Cy$$

$$\frac{Cx}{Cy} = \frac{10}{3}$$

10x in X ----------- 3x in Y

One fifth of 10x = 2x
Two third of 3x = 2x capacity available x

So x is transfered from X to Y quanity left x

thus, $$\frac{x}{10x} = \frac{1}{10}$$
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Re: Two equally sized jugs full of water are each emptied into t [#permalink]

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02 Apr 2014, 22:06
1/5 of jug X = 2/3 of jug Y
We have to fill 1/3 more of jug Y, which is therefore 1/10 of jug X
=> Proportion of jug X that will remain filled = 1/5 - 1/10 = 1/10

Option (D).
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Re: Two equally sized jugs full of water are each emptied into t [#permalink]

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Re: Two equally sized jugs full of water are each emptied into t [#permalink]

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20 Dec 2015, 01:56
GyanOne wrote:
1/5 of jug X = 2/3 of jug Y
We have to fill 1/3 more of jug Y, which is therefore 1/10 of jug X
=> Proportion of jug X that will remain filled = 1/5 - 1/10 = 1/10

Option (D).

Hey Gyanone

I do not understand how 1/3 is 1/10 of jug y

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Re: Two equally sized jugs full of water are each emptied into t [#permalink]

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30 Dec 2015, 22:02
1/5x=2/3y

x/y=10/3

so (1/3)*3=1 unit is free in Y and (1/5)*10=2 units X can give Y

1/10 leaves in X after pouring Y

D

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Re: Two equally sized jugs full of water are each emptied into t [#permalink]

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16 Feb 2017, 23:18
My 2 Cents:
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X & Y.png [ 17.63 KiB | Viewed 1249 times ]

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Re: Two equally sized jugs full of water are each emptied into t [#permalink]

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21 Feb 2017, 17:46
Can someone please explain this question with the numbers? Iam not understanding the first line given in the question. They say the jar had equal capacity before pouring into x and y right?Then why are the capacity equal to each other after pouring??

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Re: Two equally sized jugs full of water are each emptied into t [#permalink]

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21 Feb 2017, 18:52
apoorvarora wrote:
Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/5 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?

A. 0
B. 1/15
C. 2/15
D. 1/10
E. 2/10

I have tried solving it using no's...Unable to get the right answer.Can anyone elaborate please?

if 1/5*X=2/3*Y,
then 1/10*X=1/3*Y, which will fill Y,
leaving 1/5*X-1/10*X=1/10 of X containing water

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Re: Two equally sized jugs full of water are each emptied into t [#permalink]

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27 Jun 2017, 05:00
Bunuel wrote:
apoorvarora wrote:
Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/5 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?

A. 0
B. 1/15
C. 2/15
D. 1/10
E. 2/10

I have tried solving it using no's...Unable to get the right answer.Can anyone elaborate please?

There are equal amounts of water in jars X and Y, say 2L, then:
The capacity of jar X is 10L (1/5*10=2L).
The capacity of jar Y is 3L (2/3*3=2L).

Now, in order jar Y to be full we need to pour 1L from jar X to jar Y, thus there will be 1L of water left in jar X, which is 1/10 of it.

The question says that the water in the unnamed jugs was equal, that is their capacity was equal and not that X and Y are equal.
Pls explain.....
Most of the solutions here say that 1/5x=2/3y....I do not understand that how..?

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Re: Two equally sized jugs full of water are each emptied into t [#permalink]

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27 Jun 2017, 05:07
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Expert's post
siddreal wrote:
Bunuel wrote:
apoorvarora wrote:
Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/5 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?

A. 0
B. 1/15
C. 2/15
D. 1/10
E. 2/10

I have tried solving it using no's...Unable to get the right answer.Can anyone elaborate please?

There are equal amounts of water in jars X and Y, say 2L, then:
The capacity of jar X is 10L (1/5*10=2L).
The capacity of jar Y is 3L (2/3*3=2L).

Now, in order jar Y to be full we need to pour 1L from jar X to jar Y, thus there will be 1L of water left in jar X, which is 1/10 of it.

The question says that the water in the unnamed jugs was equal, that is their capacity was equal and not that X and Y are equal.
Pls explain.....
Most of the solutions here say that 1/5x=2/3y....I do not understand that how..?

Where do you see that the solution says that the capacity of X and Y are equal? The solution clearly mentions that X and Y have equal amounts of water but the capacity of X is 10L and the capacity of Y is 3L.
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Re: Two equally sized jugs full of water are each emptied into t [#permalink]

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27 Jun 2017, 06:14
apoorvarora wrote:
Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/5 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?

A. 0
B. 1/15
C. 2/15
D. 1/10
E. 2/10

I have tried solving it using no's...Unable to get the right answer.Can anyone elaborate please?

Let the capacity of Jug X be X, and that of Jug Y be Y .

so 1/5 X = 2/3 Y
-> X = 10/3 Y.......................(i)

Also total volume of 2 jugs = 2/3 Y*2 = 4/3 Y
So when the Jug Y is filled fully, The amount of water left in Jug X = 4/3 Y - Y = 1/3 Y = (1/3) (3/10 X) [From (i) Y = 3/10 X] = 1/10 X

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Re: Two equally sized jugs full of water are each emptied into t [#permalink]

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27 Jun 2017, 06:34
apoorvarora wrote:
Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/5 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?

A. 0
B. 1/15
C. 2/15
D. 1/10
E. 2/10

I have tried solving it using no's...Unable to get the right answer.Can anyone elaborate please?

p = X/5 = 2Y/3
Y/3 water is required
X/5-Y/3 Water Poured
x/5-x/10=x/10

D
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Two equally sized jugs full of water are each emptied into t [#permalink]

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27 Jun 2017, 10:44
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IMO, I think plugging number is the best approach to this sort of problem, especially for the not so confident test taker. Bunuel has given a variety of the this in a post above. Here is a similar, but IMO more foolproof approach.

1. Look for a number that is a multiple of all the integers, in the question, i.e 2*3*5 = 30.
2. Now, take this number as the equal starting volume and the find the capacity of each new jug.
1/5(X) = 30, X= 150
2/3(Y) = 30, Y= 45

3. Now take 15 from X to fill Y up. This leaves 15 in X.
30+15 = 45 ( Fills up Y)
30-15 = 15 ( Remains in X)

4. Fraction of water remaining in X = 15/150 = 1/10 (D)

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Two equally sized jugs full of water are each emptied into t [#permalink]

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27 Jun 2017, 20:43
Let the two equally sized jugs contain 2 liters of water ,
Now water is poured in two unequalempty jugs
2/x=1/5 and 2/y=2/3
solving above we have capacities of x=10 and y=3
Now y contains 2 liters of water so it needs only 1 liter to get full.
From X we take 1 liter , so the water now remaining in X is 1 liter so the fraction of water left is 1/10
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Re: Two equally sized jugs full of water are each emptied into t [#permalink]

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27 Jun 2017, 21:42
apoorvarora wrote:
Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/5 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?

A. 0
B. 1/15
C. 2/15
D. 1/10
E. 2/10

I have tried solving it using no's...Unable to get the right answer.Can anyone elaborate please?

1. Let us take the amount of water emptied as 10 L + 10 L i.e., jug x and jug y contain 10 L each
2. Jug x is 1/5 full i.e., capacity of jug x is 10*5=50 L
3. Jug y is is 2/3 full i.e., capacity of jug y is 10*3/2=15 L.
4. Five more liters will make jug y full.
5. After pouring 5 L, water left in jug x is 5 L.
6. Fraction of water contained in jug x is 5/50 = 1/10
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Re: Two equally sized jugs full of water are each emptied into t   [#permalink] 27 Jun 2017, 21:42
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