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# A total of 5 liters of gasoline is to be poured into two empty contain

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A total of 5 liters of gasoline is to be poured into two empty contain [#permalink]

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23 May 2016, 21:56
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A total of 5 liters of gasoline is to be poured into two empty containers with capacities of 2 liters and 6 liters, respectively, such that both containers will be filled to the same percent of their respective capacities. What amount of gasoline, in liters, must be poured into the 6-liter container?

A. 4$$\frac{1}{2}$$

B. 4

C. 3$$\frac{3}{4}$$

D. 3

E. 1$$\frac{1}{4}$$
[Reveal] Spoiler: OA

Last edited by Bunuel on 16 Oct 2016, 01:54, edited 1 time in total.
Renamed the topic and edited the question.

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Re: A total of 5 liters of gasoline is to be poured into two empty contain [#permalink]

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23 May 2016, 23:18
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Let x be the amount of gasoline in 2 lt container.

(x/2)*100 = ((5 - x)/6)*100
x = (5 - x)/3
3x = 5 - x
x = 1.25

Amount of gasoline in 6 lt container = 5 - 1.25 = 3.75

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Re: A total of 5 liters of gasoline is to be poured into two empty contain [#permalink]

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24 May 2016, 05:20
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nalinnair wrote:
A total of 5 liters of gasoline is to be poured into two empty containers with capacities of 2 liters and 6 liters, respectively, such that both containers will be filled to the same percent of their respective capacities. What amount of gasoline, in liters, must be poured into the 6-liter container?
A. 4$$\frac{1}{2}$$
B. 4
C. 3$$\frac{3}{4}$$
D. 3
E. 1$$\frac{1}{4}$$

Let x be the amount of solution in 6lit container and (5-x) is the amount in 2 lit solution.

The question stem says that both containers are filled to equal % of their capacity

x is what % of 6= 100x/6
5-x is what % of 2= 100 (5-x)/2

100x/6= 100(5-x)/2
x= 15/4= 3$$\frac{3}{4}$$

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Re: A total of 5 liters of gasoline is to be poured into two empty contain [#permalink]

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24 May 2016, 05:48
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nalinnair wrote:
A total of 5 liters of gasoline is to be poured into two empty containers with capacities of 2 liters and 6 liters, respectively, such that both containers will be filled to the same percent of their respective capacities. What amount of gasoline, in liters, must be poured into the 6-liter container?
A. 4$$\frac{1}{2}$$
B. 4
C. 3$$\frac{3}{4}$$
D. 3
E. 1$$\frac{1}{4}$$

Hi,

Another way-

since the different capacity containers contain same proportion, it will be the SAME as proportion in SUM of these quantities..
so Proportion is 5 liters in (2+6) or 8 ltr container......so $$Proportion = \frac{5}{8}$$...
with this proportion quantity in 6 ltr container = $$6*\frac{5}{8}= \frac{15}{4} = 3 \frac{3}{4}$$
C
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Re: A total of 5 liters of gasoline is to be poured into two empty contain [#permalink]

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24 May 2016, 07:53
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5 Litres has to be Divided into containers with total capacity 8 Lites (6 + 2) i.e 5/8.

So, 6 Litre container will have 6 * 5/8 = 15/4 or option C.

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A total of 5 liters of gasoline is to be poured into two empty contain [#permalink]

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24 May 2016, 13:52
A total of 5 liters of gasoline is to be poured into two empty containers with capacities of 2 liters and 6 liters, respectively, such that both containers will be filled to the same percent of their respective capacities. What amount of gasoline, in liters, must be poured into the 6-liter container?

A. 41212

B. 4

C. 33434

D. 3

E. 114

let x=% of capacity
5=2x+6x=8x
x=5/8
5/8*6=3 3/4 liters
C

Last edited by gracie on 09 Oct 2017, 10:08, edited 1 time in total.

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Re: A total of 5 liters of gasoline is to be poured into two empty contain [#permalink]

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15 Oct 2016, 23:07
Let x be percent filled - both to same capacity

2x + 6x= 5
8x=5
x=0.625

0.625 *6 = 3.750 => 3 3/4 since 3/4 = 0.75

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Re: A total of 5 liters of gasoline is to be poured into two empty contain [#permalink]

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19 Feb 2017, 20:34
Another way to do this problem is to WORK BACKWARDS.
Now if u pick 4, that means 4 liters go into the 6 liter container and 1 liter goes into the 2 liter container. So that is 2/3 of capacity in 6l container and 1/2 capacity in 2l container.
Now work with 3. 3 in 6l and 2 in 2l. That is, 1/2 of capacity in 6l and full capacity in 2l.
Now for 4, 6l went greater than 2l in % capacity and when we used 3, 2l container went in greater % of capacity.
Hence the only option that would satisfy this is 3 3/4 which lies in the middle of these capacities!

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Re: A total of 5 liters of gasoline is to be poured into two empty contain [#permalink]

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20 Feb 2017, 04:34
chetan2u wrote:
nalinnair wrote:
A total of 5 liters of gasoline is to be poured into two empty containers with capacities of 2 liters and 6 liters, respectively, such that both containers will be filled to the same percent of their respective capacities. What amount of gasoline, in liters, must be poured into the 6-liter container?
A. 4$$\frac{1}{2}$$
B. 4
C. 3$$\frac{3}{4}$$
D. 3
E. 1$$\frac{1}{4}$$

Hi,

Another way-

since the different capacity containers contain same proportion, it will be the SAME as proportion in SUM of these quantities..
so Proportion is 5 liters in (2+6) or 8 ltr container......so $$Proportion = \frac{5}{8}$$...
with this proportion quantity in 6 ltr container = $$6*\frac{5}{8}= \frac{15}{4} = 3 \frac{3}{4}$$
C

Hi chetan your explanation is easy can you please tell if it will be for smaller container will the logic be 2*5/8 mean 5/4 or 1*1/4 ??
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Re: A total of 5 liters of gasoline is to be poured into two empty contain [#permalink]

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25 Feb 2017, 01:59
Let x litre be added in 2 litre container and 5-x added to 6 litre container

x/2=(5-x)/6

x=5/4 .....water added 5-x = 5-5/4 =15/4

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Re: A total of 5 liters of gasoline is to be poured into two empty contain [#permalink]

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11 Mar 2017, 12:09
I tried to work from backwards and got an answer in cca. 15 sec
first tested D: what was not enough
then B: too much
C was fine

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Re: A total of 5 liters of gasoline is to be poured into two empty contain [#permalink]

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08 Oct 2017, 19:07
Let's say z is the percentage that both bottles are supposed to be. That means:

Quote:
(x/2) = z
(y/6) = z

In other words

Quote:
(x/2) = (y/6)
which means x = (1/3)y

The amounts in both bottles must equal 5 so

Quote:
x+y = 5
(1/3)y + y = 5
(4/3)y = 5

Now you can solve for y, which is the amount in the larger bottle

Quote:
y = 5(3/4) = (15/4) = 3 and (3/4)

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Re: A total of 5 liters of gasoline is to be poured into two empty contain [#permalink]

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12 Oct 2017, 17:04
nalinnair wrote:
A total of 5 liters of gasoline is to be poured into two empty containers with capacities of 2 liters and 6 liters, respectively, such that both containers will be filled to the same percent of their respective capacities. What amount of gasoline, in liters, must be poured into the 6-liter container?

A. 4$$\frac{1}{2}$$

B. 4

C. 3$$\frac{3}{4}$$

D. 3

E. 1$$\frac{1}{4}$$

Solution:

Since the 6-liter container is 3 times the capacity of the 2-liter container, we want to pour 3 times as much gasoline into the 6-liter container as into the 2-liter container. We can let x = the amount of gasoline poured into the 2-liter container; thus, 3x = the amount of gasoline poured into the 6-liter container. We can solve for x using the following equation:

x + 3x = 5

4x = 5

x = 5/4

Thus, the amount of gasoline that should be poured into the 6-liter container is 3 x 5/4 = 15/4 = 3 ¾ liters.

Alternate Solution:

Let x denote the amount of gasoline poured into the 6-liter container. Since the percentages of gasoline in each container must be the same, we must have:

x/6 = (5-x)/2

2x = 30 - 6x

8x = 30

x = 30/8 = 3 ¾

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Re: A total of 5 liters of gasoline is to be poured into two empty contain [#permalink]

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13 Oct 2017, 02:46
Using Ratio and Proportions,

2x + 6x = 5 lts
8x=5
x = 0.625
and hence 6x = 3.75 i.e 3 3/4

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Re: A total of 5 liters of gasoline is to be poured into two empty contain [#permalink]

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14 Dec 2017, 04:29
If you focus on keyword " Same proportion in each container " you can get away with right solution without solving.

Use logic.
You have 5 liters and two containers 2 liters(Call it X) & 6 liters each. (Call it Y)

If you go half and half with both. 1 liter would be left out. ( 1 liter poured in X & 3 liters Poured in Y, which makes total of 4)

So obviously you will have to increase input in X and henceforth it will allow you to increase input in Y. ( Same proportion limit in stem)

Thinking this way will help eliminate all options and only C will be left.

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Re: A total of 5 liters of gasoline is to be poured into two empty contain   [#permalink] 14 Dec 2017, 04:29
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