Two-fifths of the volume of a mixture of milk and water of ratio 4:3 is
converted into a mixture of ratio 5:3 by the method of replacement with milk.
The 4:3 mixture was prepared from a 4:1 mixture by addition of water. If the
replacement milk volume is 14 litres, what was the volume of the water added
to make the original mixture?
Pick ONE option
A) 12 litres
B) 60 litres
C) 80 litres
D) 24 litres
Clear Selection
Answers
Given : Two-fifths of the volume of a mixture of milk and water of ratio 4:3 is converted into a mixture of ratio 5:3 by the method of replacement with milk. Replacement milk volume is 14 litres
The 4:3 mixture was prepared from a 4:1 mixture by addition of water.
To Find : volume of the water added to make the original mixture
A) 12 litres
B) 60 litres
C) 80 litres
D) 24 litres
Solution:
Original Mixture 4: 1
MIlk = 4X litre
Water = X litre
Water added = Y litre
=> Milk = 4X , water = X + Y
Ratio = 4 : 3
=> 4X / ( X + Y) = 4/3
=> 3X = X + Y
=> 2X = Y
Milk = 4X
Water = 3X
Mixture = 7X
Two-fifths of the volume of a mixture of milk
= (2/5)7X
= 14X/5
MILK = 8X/5
WATER = 6X/5
converted into a mixture of ratio 5:3 by the method of replacement with milk. replacement milk volume is 14 litres,
14 litre has (4/7)14 = 8 litre milk and 6 litre water
MILK = 8X/5 - 8 + 14 = 8X/5 + 6 = (8X + 30)/5
WATER = 6X/5 - 6 = (6X - 30)/5
Ratio = 5 : 3
=> (8X + 30) / (6X - 30) = 5/3
=> 24X + 90 = 30X - 150
=> 6X = 240
=> X = 40
Original mixture has 40 Litre Water
Info :
Original mixture MILK 160 WATER 40 Ratio 4 : 1
Water Added = 80 LITRE
Now Mixture MILK 160 WATER 120 Ratio 4 : 3
2/5 of Mixture MILK 64 WATER 48 Ratio 4 : 3
replacement with 14 Litre milk
14 Litre has 8 LITRE MILK and 6 LITRE WATER
FINAL MIXTURE 64 - 8 + 14 = 70 WATER = 48 - 6 = 42
70 : 42 = 5 : 3
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