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Two containers of equal capacity are full of a mixture of oil and wat

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Two containers of equal capacity are full of a mixture of oil and wat [#permalink]

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New post 17 May 2011, 11:27
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Two containers of equal capacity are full of a mixture of oil and water . In the first, the ratio of oil to water is 4:7 and in the second it is 7:11. Now both the mixtures are mixed in a bigger container. What is the resulting ratio of oil to water.

a. 149 : 247
b. 247 : 149
c. 143 : 241
d. 241 : 143
[Reveal] Spoiler: OA

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Re: Two containers of equal capacity are full of a mixture of oil and wat [#permalink]

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New post 17 May 2011, 11:50
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4: 7 means oil/ (oil+water) = 4/(7+4) = 4/11 similarly 7:11 means 7/18 for oil in B.
LCM = 11*18 = volume stored in each tank.

oil in A = 4/11 * (11*18) = 72 oil in B = 7/18 * (11*18) = 77 total oil = 72+79 = 149

water in A = 7/11(11*18) = 126 water in B = 11/18 * (11*18) = 121 total water = 126 + 121 = 247

hence A 149:247
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Re: Two containers of equal capacity are full of a mixture of oil and wat [#permalink]

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New post 17 May 2011, 11:58
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amit2k9 wrote:
4: 7 means oil/ (oil+water) = 4/(7+4) = 4/11 similarly 7:11 means 7/18 for oil in B.
LCM = 11*18 = volume stored in each tank.

oil in A = 4/11 * (11*18) = 72 oil in B = 7/18 * (11*18) = 77 total oil = 72+79 = 149

water in A = 7/11(11*18) = 126 water in B = 11/18 * (11*18) = 121 total water = 126 + 121 = 247

hence A 149:247


Thanks, :) but I have a doubt, :( why you took the LCM ?

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New post 17 May 2011, 12:10
Easier for calculation here.

4/11 and 7/18 ..denominators cancel 11*18 giving integer values for Oil and Water quantity.
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Re: Two containers of equal capacity are full of a mixture of oil and wat [#permalink]

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New post 17 May 2011, 12:18
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Two Container C1, C2 of equal capacity x.

For C1:
Oil= 4/11 x
Water= 7/11 x

For C2
Oil= 7/18 x
Water = 7/11 x

Mix C1 and C2.
Total Oil= 4/11 x + 7/18 x = 149/198 x
Total Water= 7/11 x + 7/11 x = 247/198 x

resulting ratio of oil to water = (149/198 x) / (247/198 x)
= 149:247.
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Re: Two containers of equal capacity are full of a mixture of oil and wat [#permalink]

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New post 17 May 2011, 16:27
O1 = (4/11)(O1+W1)

W1 = (7/11)(O1+W1)

O2 = (7/18)(02+W2)

W2 = (11/18)(O2+W2)


O/W = (01+W1)/02+W2) = ((4/11)+(7/11))/((7/18)+(11/18)) [ EQUAL CAPACITY i.e O1+W1 = O2+W2 , so they
cancel out in numerator and denominator]

=149/247

Answer is A.

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Re: Two containers of equal capacity are full of a mixture of oil and wat [#permalink]

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Re: Two containers of equal capacity are full of a mixture of oil and wat [#permalink]

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New post 15 May 2016, 07:30
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Re: Two containers of equal capacity are full of a mixture of oil and wat [#permalink]

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New post 20 May 2017, 05:57
ramkryp wrote:
Two containers of equal capacity are full of a mixture of oil and water . In the first, the ratio of oil to water is 4:7 and in the second it is 7:11. Now both the mixtures are mixed in a bigger container. What is the resulting ratio of oil to water.

a. 149 : 247
b. 247 : 149
c. 143 : 241
d. 241 : 143


Can this question be done through allegation? thanks

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Two containers of equal capacity are full of a mixture of oil and wat [#permalink]

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New post 01 Jun 2017, 09:27
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OreoShake wrote:
ramkryp wrote:
Two containers of equal capacity are full of a mixture of oil and water . In the first, the ratio of oil to water is 4:7 and in the second it is 7:11. Now both the mixtures are mixed in a bigger container. What is the resulting ratio of oil to water.

a. 149 : 247
b. 247 : 149
c. 143 : 241
d. 241 : 143


Can this question be done through allegation? thanks


when i read: "Two containers of equal capacity"...
then:
first container 4:7 so capacity 4+7 = 11
second container 7:11 so capacity 7+11 = 18

to create an equal capacity that would be easier to work with:
11*18 = 198 in each container

looking at the results i need the capacity of the two containers, so:
198*2 = 396

answer a fits perfect:
a. 149 : 247 -- 149+247 = 396

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Re: Two containers of equal capacity are full of a mixture of oil and wat [#permalink]

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New post 01 Jun 2017, 09:38
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ramkryp wrote:
Two containers of equal capacity are full of a mixture of oil and water . In the first, the ratio of oil to water is 4:7 and in the second it is 7:11. Now both the mixtures are mixed in a bigger container. What is the resulting ratio of oil to water.

a. 149 : 247
b. 247 : 149
c. 143 : 241
d. 241 : 143


This is not an Official Guide question and cannot be. It has 4 options instead of 5. Tag removed.
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Re: Two containers of equal capacity are full of a mixture of oil and wat [#permalink]

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New post 01 Sep 2017, 23:51
I solved this question in a slightly different but much easier way.

I plugged in a value for the amount of each mixture added, which happens to be equal since the same amount is added.
To choose a good number I converted the Oil:Water ratio to a Oil:Solution ratio, by merely adding the numerator to the denominator, since the solution = Oil + Water.

Therefore, the two Oil:Solution ratios are = 4:11, and 7:18 respectively.
Then I picked a number which is divisible both by 11 and 18 = 11 x 18 = 198. (This gives us an easy answer for the Oil in each mixture)

Therefore
The amount of Oil in Mixture 1 = 4 x 198 / 11 = 4 x 18 = 72.
The amount of Oil in Mixture 2 = 7 x 198 / 18 = 7 x 11 = 77.
Total of Oil in the Final Mixture = 77 + 72 = 149

Total Volume of Final Mixture = 198 + 198 = 396.
Total Water in the Final Mixture = 396 - 149 = 247

Therefore, Answer = Total water / Total oil = 149/247
Answer = A

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Re: Two containers of equal capacity are full of a mixture of oil and wat   [#permalink] 01 Sep 2017, 23:51
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