Ratio of quantity of milk and water in a ____ litre

Solution

From (I) - Initial quantity of milk in the mixture = {140 X (4/7)} = 80 litres And initial quantity of water in the mixture = (140 - 80) = 60 litres Quantity of milk left in the mixture after taking out 25% of milk = 0.75 X 80 = 60 litres Quantity of water left in the mixture after taking out 25% of water = 0.75 X 60 = 45 litres Final quantity of water in the mixture = 45 + 15 = 60 litres Here, final quantity of water is equal to the quantity of milk. So, I is false. From (II) - Initial quantity of milk in the mixture = {196 X (4/7)} = 112 litres And initial quantity of water in the mixture = (196 - 112) = 84 litres Quantity of milk left in the mixture after taking out 25% of milk = 0.75 X 112 = 84 litres Quantity of water left in the mixture after taking out 25% of water = 0.75 X 84 = 63 litres Final quantity of water in the mixture = 63 + 12 = 75 litres Required percentage = {(84 - 75)/84} X 100 = (75/7)% less So, II is true. From (III) - Initial quantity of milk in the mixture = {224 X (4/7)} = 128 litres And initial quantity of water in the mixture = (224 - 128) = 96 litres Quantity of milk left in the mixture after taking out 25% of milk = 0.75 X 128 = 96 litres Quantity of water left in the mixture after taking out 25% of water = 0.75 X 96 = 72 litres Final quantity of water in the mixture = 72 + 44 = 116 litres Required percentage = {(116 - 96)/96} X 100 = (125/6)% more So, III is true. From (IV) - Initial quantity of milk in the mixture = {280 X (4/7)} = 160 litres And initial quantity of water in the mixture = (280 - 160) = 120 litres Quantity of milk left in the mixture after taking out 25% of milk = 0.75 X 160 = 120 litres Quantity of water left in the mixture after taking out 25% of water = 0.75 X 120 = 90 litres Final quantity of water in the mixture = 90 + 20 = 110 litres Required percentage = {(120 - 110)/120} X 100 = (25/3)% less So, IV is true. Hence, option d.