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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 6liter container? A. 4\(\frac{1}{2}\) B. 4 C. 3\(\frac{3}{4}\) D. 3 E. 1\(\frac{1}{4}\)
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Originally posted by nalinnair on 23 May 2016, 22:56.
Last edited by Bunuel on 16 Oct 2016, 02:54, 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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24 May 2016, 00:18
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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
Answer: 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, 06:20
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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 6liter 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 (5x) 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 5x is what % of 2= 100 (5x)/2 100x/6= 100(5x)/2 x= 15/4= 3\(\frac{3}{4}\) C is the answer
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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, 06:48
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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 6liter 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, 08:53
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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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Updated on: 09 Oct 2017, 11:08
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 6liter 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, 14:52.
Last edited by gracie on 09 Oct 2017, 11:08, 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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16 Oct 2016, 00:07
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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, 21:34
Another way to do this problem is to WORK BACKWARDS. Start with the two easy numbers 4 and 3. 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, 05:34
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 6liter 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, 02:59
Let x litre be added in 2 litre container and 5x added to 6 litre container
x/2=(5x)/6
x=5/4 .....water added 5x = 55/4 =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, 13:09
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, 20:07
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, 18:04
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 6liter container?
A. 4\(\frac{1}{2}\)
B. 4
C. 3\(\frac{3}{4}\)
D. 3
E. 1\(\frac{1}{4}\) Solution: Since the 6liter container is 3 times the capacity of the 2liter container, we want to pour 3 times as much gasoline into the 6liter container as into the 2liter container. We can let x = the amount of gasoline poured into the 2liter container; thus, 3x = the amount of gasoline poured into the 6liter 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 6liter container is 3 x 5/4 = 15/4 = 3 ¾ liters. Alternate Solution: Let x denote the amount of gasoline poured into the 6liter container. Since the percentages of gasoline in each container must be the same, we must have: x/6 = (5x)/2 2x = 30  6x 8x = 30 x = 30/8 = 3 ¾ Answer: 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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13 Oct 2017, 03:46
Using Ratio and Proportions,
2x + 6x = 5 lts 8x=5 x = 0.625 and hence 6x = 3.75 i.e 3 3/4
Henc answer is 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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14 Dec 2017, 05:29
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]
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29 Mar 2018, 12:12
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 6liter 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 ?



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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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29 Mar 2018, 17:36
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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 6liter 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 2ltr can should have 40% gasoline and remaining gasoline should be in 6litre can. What is the proportion of gasoline in 6ltr can? Here 40% in 2ltr means 40*2/100=0.8 So remaining 50.8=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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30 Mar 2018, 12:47
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
Answer: C 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?



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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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31 Mar 2018, 03:18
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
Answer: C 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 dave13So, 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, 5x goes into the other container. So, we get the equation \(\frac{x}{2}*100 = \frac{5x}{6}*100\) Hope this clears your confusion.
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