Question
The ratio of quantity of milk to that of water in a 48
litre of mixture is 3:1. If 'x' litres of mixture is replaced by same quantity of water, then the ratio of quantity of milk and water becomes 2:1, respectively. Find the value of 'x'.Solution
Let the quantity of milk and water in the mixture be '3a' litres and 'a' litres, respectively. So, total quantity of milk in the mixture = (3a/4a) × 48 = 36 litres total quantity of water in the mixture = (a/4a) × 48 = 12 litres Let the total quantity of water taken out be 'b' litres. Then, total quantity of milk taken out = (x - b) litres ATQ, (x - b):b = 3:1 Or, x - b = 3b Or, x = 4b....(i) Now, {36 - (4b - b)}:(12 - b + 4b) = 2:1 Or, 36 - 3b = 24 + 6b Or, 9b = 12 So, 'b' = 4/3 From equation (i) 'x' = 4b = 4 × 4/3 = 5.33
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