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08 Mar 2021, 09:45
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
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Question Stats:
71% (02:53) correct
29%
(03:17)
wrong
based on 189
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18 litres of pure water was added to a vessel containing 80 litres of pure milk. 49 litres of the resultant mixture was then sold and some more quantity of pure milk and pure water was added to the vessel in the ratio of 2 : 1. If the resultant ratio of milk to water in the vessel was 4 : 1, what was the quantity of pure milk added to the vessel ? (in litres)
(A) 4
(B) 6
(C) 12
(D) 16
(E) 18
(A) 4
(B) 6
(C) 12
(D) 16
(E) 18
08 Mar 2021, 15:06
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Bunuel
18 litres of pure water was added to a vessel containing 80 litres of pure milk. 49 litres of the resultant mixture was then sold and some more quantity of pure milk and pure water was added to the vessel in the ratio of 2 : 1. If the resultant ratio of milk to water in the vessel was 4 : 1, what was the quantity of pure milk added to the vessel ? (in litres)
(A) 4
(B) 6
(C) 12
(D) 16
(E) 18
(A) 4
(B) 6
(C) 12
(D) 16
(E) 18
Initially, we had: milk = 80, water = 18
Total quantity = 98 litres
Quantity Sold = 49 litres, which is half of the total volume
Thus, each of milk and water would become half their respective volumes; i.e. milk = 40, water = 9
Milk : water added = 2 : 1
Say Milk added = 2x and water added = x
Thus, final milk = 40+2x and water = 9+x
This ratio is 4:1
Hence: (40+2x)/(9+x) = 4/1
x = 2
Thus, milk added = 2x = 4 litres
Answer A
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General Discussion
15 Mar 2021, 16:49
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The answer is B:
The original mix is 80:18, which is a 40:9 ratio. So when 49 is removed from the original we are left with literally that exact proportion. Then we add 2:1 mixture until it becomes 4/1. In other words, every 2 portions out 3 of the new mixture is milk and every 1 portions out of 3 is water. Therefore we can use the following logic:
Current Milk/Current water = 40/9
(Current Milk + (2/3)x)/(Current Water +(1/3)x) = 4/1
(40+(2/3)x)/(9+(1/3)x) = 4/1
40+(2/3)x = 36+(4/3)x
4 = (4/3)x - (2/3)x
4 = (2/3)x
6 = x
We can double check by inserting x back into the formula, we see that 40+(2/3)*6 = 44 and 9+(1/3)*6 = 11 which is a 44:11 or 4:1 ratio. Easy Peasy.
The original mix is 80:18, which is a 40:9 ratio. So when 49 is removed from the original we are left with literally that exact proportion. Then we add 2:1 mixture until it becomes 4/1. In other words, every 2 portions out 3 of the new mixture is milk and every 1 portions out of 3 is water. Therefore we can use the following logic:
Current Milk/Current water = 40/9
(Current Milk + (2/3)x)/(Current Water +(1/3)x) = 4/1
(40+(2/3)x)/(9+(1/3)x) = 4/1
40+(2/3)x = 36+(4/3)x
4 = (4/3)x - (2/3)x
4 = (2/3)x
6 = x
We can double check by inserting x back into the formula, we see that 40+(2/3)*6 = 44 and 9+(1/3)*6 = 11 which is a 44:11 or 4:1 ratio. Easy Peasy.
