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Three containers A, B and C are having mixtures of milk and water in the ratio 1 : 5, 3 : 5 and 5 : 7, respectively. If the capacities of the containers are in the ratio 5 : 4 : 5, find the ratio of milk to water, if the mixtures of all the three containers are mixed together ?
(A) 53 : 115
(B) 23 : 123
(C) 11 : 4
(D) 17 : 23
(E) None of these
Are You Up For the Challenge: 700 Level Questions
(A) 53 : 115
(B) 23 : 123
(C) 11 : 4
(D) 17 : 23
(E) None of these
Are You Up For the Challenge: 700 Level Questions
12 Jan 2022, 02:40
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Looking at the various ratios, A:B:C sizes are in the ratio of 5:4:5 and each have a ratio of milk to water respectively of 1:5, 3:5 and 5:7. Which means A's total mixture is a value which is divisible by 6, B's is divisible by 8 and C's is divisible by 12.
Looking at A and C alone, 120 liters is a good size to work with. Let A be 120 liters big, let B also be 120 liters big, which then means that C will be 96 liters big. (the ratio of A:B:C is multiplied right through by 24 to set a size to each container)
As the sizes have been set, now one can add actual liter values to the respective milk to water ratios:
Container A: 120 liters in the ratio 1:5 becomes 20l of milk and 100l of water.
Container B: 96 liters in the ratio 3:5 becomes 36l of milk and 60l of water.
Container C: 120 liters in the ratio 5:7 becomes 50l of milk and 70l of water.
Summing the milk and water: Milk: \(20+36+50 = 106\) Water:\(100+60+70 = 230\)
Ratio of milk to water = 106:230 which when simplified is 53:115
Answer A
Looking at A and C alone, 120 liters is a good size to work with. Let A be 120 liters big, let B also be 120 liters big, which then means that C will be 96 liters big. (the ratio of A:B:C is multiplied right through by 24 to set a size to each container)
As the sizes have been set, now one can add actual liter values to the respective milk to water ratios:
Container A: 120 liters in the ratio 1:5 becomes 20l of milk and 100l of water.
Container B: 96 liters in the ratio 3:5 becomes 36l of milk and 60l of water.
Container C: 120 liters in the ratio 5:7 becomes 50l of milk and 70l of water.
Summing the milk and water: Milk: \(20+36+50 = 106\) Water:\(100+60+70 = 230\)
Ratio of milk to water = 106:230 which when simplified is 53:115
Answer A
12 Jan 2022, 05:48
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Percentage of milk in 1st, 2nd and 3rd containers are
5x*(1/6),4x*(3/8),5x*(5/12)
Percentage of water in 1st,2nd and 3rd containers are
5x*(5/6), 4x*(5/8), 5x*(7/12)
In mixture, total amount of milk = 53x/12
Total amount of water = 115x/12
So, ratio of milk and water in the mixture =(53x/12)/(115x/12)=53:115
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5x*(1/6),4x*(3/8),5x*(5/12)
Percentage of water in 1st,2nd and 3rd containers are
5x*(5/6), 4x*(5/8), 5x*(7/12)
In mixture, total amount of milk = 53x/12
Total amount of water = 115x/12
So, ratio of milk and water in the mixture =(53x/12)/(115x/12)=53:115
Posted from my mobile device
