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by vaibhav101 » Thu May 31, 2018 8:26 am

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Difficulty—

3 containers have their volumes in the ratio 3:4:5.. They are full of mixtures of milk and water. The mixture contain milk and water in the ratio of (4:1), (3:1) and (5:2) respectively. the contents of all these 3 containers are poured into a fourth container. the ratio of milk and water in the 4th container is

A 4:1
B 151:48
C 157:53
D 5:2
E none of these
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by [email protected] » Thu May 31, 2018 6:30 pm
Hi vaibhav101,

We're told that 3 containers have their volumes in the ratio 3:4:5 and the 3 mixtures contain milk and water in the ratio of (4:1), (3:1) and (5:2) respectively. We're asked for the ratio of all milk to all water in the 3 containers. This question can be solved in a couple of different ways, including by TESTing VALUES.

The most 'ugly' of the 3 ratios is 5:2 (for every 5 parts of milk, there are 2 parts of water - with a total of 7 parts). With the given 3:4:5 ratio of total volumes, we can set the largest volume to 35 liters (which is 5x7, and will help make the math for the other containers a bit easier to deal with). Thus, the ratio of the volumes will be 21:28:35.

IF....
the containers hold 21 liters, 28 liters and 35 liters respectively, then
the 1st container holds (4/5)(21) liters of milk and (1/5)(21) liters of water
the 2nd container holds (3/4)(28) liters of milk and (1/4)(28) liters of water
the 3rd container holds (5/7)(35) liters of milk and (2/7)(35) liters of water

Total milk = 84/5 + 21 + 25 =
84/5 + 46 =
84/5 + 230/5
314/5
Total water = 21/5 + 7 + 10 =
21/5 + 17 =
21/5 + 85/5 =
106/5
Thus, the ratio of total milk to total water = (314/5)/(106/5) = 314/106 = 157/53

Final Answer: C

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3 containers

by GMATGuruNY » Fri Jun 01, 2018 3:02 am
vaibhav101 wrote:3 containers have their volumes in the ratio 3:4:5.. They are full of mixtures of milk and water. The mixture contain milk and water in the ratio of (4:1), (3:1) and (5:2) respectively. the contents of all these 3 containers are poured into a fourth container. the ratio of milk and water in the 4th container is

A 4:1
B 151:48
C 157:53
D 5:2
E none of these
Container 1 : Container 2 : Container 3 = 3:4:5.

In Container 1, M:W = 4:1, implying that water constitutes 1/5 of Container 1.
In Container 2, M:W = 3:1, implying that water constitutes 1/4 of Container 2.
In Container 3, M:W = 5:2, implying that water constitutes 2/7 of Container 3.

The LCM for the denominators of the blue fractions = 5*4*7 = 140.
To make the math easier, multiply the red ratio by this LCM:
Container 1: Container 2: Container 3 = 3(140) : 4(140) : 5(140) = 420:560:700.
Resulting total volume = 420+560+700 = 1680.

Applying the blue fractions to 420:560:700, we get:
Water in Container 1 = (1/5)(420) = 84.
Water in Container 2 = (1/4)(560) = 140.
Water in Container 3 = (2/7)(700) = 200.
Total water = 84 + 140 + 200 = 424.
Thus:
Total milk = (total volume) - (total water) = 1680 - 424 = 1256.
Resulting ratio:
M:W = 1256:424 = 157:53.

The correct answer is C.
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by Jeff@TargetTestPrep » Sun Jun 03, 2018 5:33 pm
vaibhav101 wrote:3 containers have their volumes in the ratio 3:4:5.. They are full of mixtures of milk and water. The mixture contain milk and water in the ratio of (4:1), (3:1) and (5:2) respectively. the contents of all these 3 containers are poured into a fourth container. the ratio of milk and water in the 4th container is

A 4:1
B 151:48
C 157:53
D 5:2
E none of these
We can let the volume of the largest container be 35, thus the volume of the middle one is 28 and the volume of the largest one is 21.

Since the milk and water in the smallest container are in a ratio of 4:1, we have:

4x + x = 21

5x = 21

x = 4.2

So, we have milk = 16.8 and water = 4.2 in the smallest container.

Since the milk and water in the middle container are in a ratio of 3:1, we have:

3y + y = 28

4y = 28

y = 7

So, we have mike = 21 and water = 7 in the middle container.

Since the milk and water in the largest container are in a ratio of 5:2, we have:

5z + 2z = 35

7z = 35

z = 5

So, we have mike = 25 and water = 10 in the largest container.

When the contents of all these 3 containers are poured into a fourth container, we have milk = 16.8 + 21 + 25 = 62.8 and water = 4.2 + 7 + 10 = 21.2. Thus the ratio of milk and water is:

62.8/21.2 = 628/212 = 157/53

Answer: C

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