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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