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There are three vessels of equal capacity .Vessel A contains Milk and [#permalink]

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10 Oct 2011, 04:09

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There are three vessels of equal capacity .Vessel A contains Milk and water in the ratio 4:3 ;Vessel B contains Milk and water in the ratio 2:1 and Vessel C contains Milk and water in the ratio 3:2 .If the mixture in all the three vessels is mixed up.What will be the ratio of milk and water ?

Re: There are three vessels of equal capacity .Vessel A contains Milk and [#permalink]

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10 Oct 2011, 05:36

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gmatcracker24 wrote:

There are three vessels of equal capacity .Vessel A contains Milk and water in the ratio 4:3 ;Vessel B contains Milk and water in the ratio 2:1 and Vessel B contains Milk and water in the ratio 3:2 .If the mixture in all the three vessels is mixed up.What will be the ratio of milk and water ?

A)9:6 B)3:2 C)118:126 D)193:122 E)201:132

Try solving this question and share your approach .

I will share a efficient way to solve such kind of questions ,once i see some approaches.

Re: There are three vessels of equal capacity .Vessel A contains Milk and [#permalink]

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10 Oct 2011, 06:12

fluke wrote:

gmatcracker24 wrote:

There are three vessels of equal capacity .Vessel A contains Milk and water in the ratio 4:3 ;Vessel B contains Milk and water in the ratio 2:1 and Vessel B contains Milk and water in the ratio 3:2 .If the mixture in all the three vessels is mixed up.What will be the ratio of milk and water ?

A)9:6 B)3:2 C)118:126 D)193:122 E)201:132

Try solving this question and share your approach .

I will share a efficient way to solve such kind of questions ,once i see some approaches.

4:3=>4x+3x=7x 2:1=>2y+1y=3y 3:2=>3z+2z=5z

7x=3y=5z

Take LCM of 7,3,5=105

Or simply; x=3*5=15 y=7*5=35 z=3*7=21

So,

Ratio of Milk:Water= (4x+2y+3z)/(3x+y+2z)=193/122

Ans: "D"

Perfect Fluke...Bang on!! This was the approach i was taking abt +1
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There are three vessels of equal capacity .Vessel A contains Milk and water in the ratio 4:3 ;Vessel B contains Milk and water in the ratio 2:1 and Vessel B contains Milk and water in the ratio 3:2 .If the mixture in all the three vessels is mixed up.What will be the ratio of milk and water ?

A)9:6 B)3:2 C)118:126 D)193:122 E)201:132

Try solving this question and share your approach .

I will share a efficient way to solve such kind of questions ,once i see some approaches.

Here is my approach, very similar to fluke's, just a different thought process of arriving at the same calculation.

The three vessels are of equal capacity (which we assume to be full since it is a PS question. I would prefer clearer direction though). The milk:water ratio is given for each as 4:3, 2:1 and 3:2. The reason we cannot just add the milk parts (4+2+3) and water parts (3+1+2) together is that they represent different fractions of the whole volume i.e. in the first vessel, milk is 4 parts out of a total of 7 parts while in the second vessel, milk is 2 parts out of a total of 3 parts etc. If we make the total number of parts in each ratio equal, then we can just add the 'milk parts' together and all the 'water parts' together. Ratios: 4:3 (Total 7 parts) 2:1 (Total 3 parts) 3:2 (Total 5 parts) How can we make the total number of parts equal in the 3 cases? By taking the LCM. 4*15 : 3*15 = 60:45 (Total parts 105) 2*35 : 1*35 = 70:35 (Total parts 105) 3*21 : 2*21 = 63:42 (Total parts 105) When we mix the three solutions, the total number of parts of milk is 60+70+63 = 193 the total number of parts of water = 45+35+42 = 122 The required ratio = 193:122
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Re: There are three vessels of equal capacity .Vessel A contains Milk and [#permalink]

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10 Oct 2011, 11:42

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Can someone tell what is wrong with my method, which is close to the OA: Say A=B=C=100 ml Therefore, Milk in A= 57 ml (57%) B= 67 ml (66.66%) C= 60 ml (60%) Total Milk= 57+67+60= 184 ml out of 300 ml and the rest is Water = 116 ml So, the ratio is 184:116

Re: There are three vessels of equal capacity .Vessel A contains Milk and [#permalink]

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10 Oct 2011, 12:01

BDSunDevil wrote:

Can someone tell what is wrong with my method, which is close to the OA: Say A=B=C=100 ml Therefore, Milk in A= 57 ml (57%) B= 67 ml (66.66%) C= 60 ml (60%) Total Milk= 57+67+60= 184 ml out of 300 ml and the rest is Water = 116 ml So, the ratio is 184:116

Nothing wrong. Just that this is an approximation.
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Re: There are three vessels of equal capacity .Vessel A contains Milk and [#permalink]

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11 Oct 2011, 04:41

I am guessing ones you get the LCM, you divide the LCM by the number of parts the ship carrys then multiply the resultant number to the single part. For Ship 1, 4:3...7 parts 105/7=15 4*15=60 3*15=45 therefore 60:45

Right now, we can't just add the parts of milk together since the parts are not the same. 1 part of vessel 1 is smaller than 1 part of vessel 2 since the same volume in vessel 1 is divided into 7 parts but in only 3 parts in vessel 2. If we can make one part of each vessel equal, we can just add the parts. What is the LCM of 7, 3 and 5? It will be 7*3*5 (=105) since all the numbers are prime numbers.

When we multiply the entire ratio by the same number, the ratio remains unchanged.

Vessel 1 -> We need a total of 105 parts instead of 7 so we multiply by 15. The ratio becomes 4*15 : 3*15 = 60:45 Vessel 2 -> We need a total of 105 parts instead of 3 so we multiply by 35. The ratio becomes 2*35 : 1*35 = 70:35 Vessel 3 -> We need a total of 105 parts instead of 5 so we multiply by 21. The ratio becomes 3*21 : 2*21 = 63:42

Re: There are three vessels of equal capacity .Vessel A contains Milk and [#permalink]

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20 Aug 2017, 22:50

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