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

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Question Stats: 79% (01:58) correct 21% (02:08) wrong based on 1540 sessions

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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$$\frac{1}{4}$$

Originally posted by nalinnair on 23 May 2016, 21:56.
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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10
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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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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1
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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4
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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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

Originally posted by gracie on 24 May 2016, 13:52.
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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2
1
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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1
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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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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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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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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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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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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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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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]

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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

chetan2u hello what if different capacity containers contain different proportion ? can you give example please ? Math Expert V
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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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dave13 wrote:
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

chetan2u hello what if different capacity containers contain different proportion ? can you give example please ? Hi...
Dave, an example of that kind would be..
5- litres to be poured in 2 and 6 litre capacity cans. The 2-ltr can should have 40% gasoline and remaining gasoline should be in 6-litre can. What is the proportion of gasoline in 6-ltr can?

Here 40% in 2-ltr means 40*2/100=0.8
So remaining 5-0.8=4.2 in 6 ltr can..
Proportion = 4.2/6 * 100=70%
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A total of 5 liters of gasoline is to be poured into two empty contain  [#permalink]

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Vyshak wrote:
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

I have one question about above mentioned solution

(x/2)*100 = ((5 - x)/6)*100 is it a proportion ?

Does this part called ratio (x/2)*100 kindof dont get sence of the solution

when a total of 5 liters of gasoline is to be poured into two empty containers with capacities of 2 liters and 6 liters why are we dividing x by 2 the concept is kindof strange to me... whats the logic behind this division (x/2)*100 Hi pushpitkc, can you please explain the above? Senior PS Moderator V
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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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dave13 wrote:
Vyshak wrote:
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

I have one question about above mentioned solution

(x/2)*100 = ((5 - x)/6)*100 is it a proportion ?

Does this part called ratio (x/2)*100 kindof dont get sence of the solution

when a total of 5 liters of gasoline is to be poured into two empty containers with capacities of 2 liters and 6 liters why are we dividing x by 2 the concept is kindof strange to me... whats the logic behind this division (x/2)*100 Hi pushpitkc, can you please explain the above? Hi dave13

So, there are 2 empty containers(one 2 liters and another 6 liters in capacity)
A total of 5 liters is to be poured into the two containers and both must be filled
to the same percent. If x liters goes into one of the containers, 5-x goes into the
other container.

So, we get the equation $$\frac{x}{2}*100 = \frac{5-x}{6}*100$$

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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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1
good contender for backsolving: solved it in 30 secs. well no this was an afterthought A) 4.5/6 does it equal 0.5/2 (5 liters - 4.5), Nope move on

B. 4/6 does it equal 2/2 (5 liters - 4), Nope move on

C) 3.75/6 does it equal 1.25/2 (5 liters - 3.75), Yes, 1.25/2 multiply 3 both with denominator and numerator. This is right.

Less Brain Power utilized too.
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My glory is greater than my life. Re: A total of 5 liters of gasoline is to be poured into two empty contain   [#permalink] 16 Jun 2018, 06:09

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