Ratio of quantity of milk and water in a ____ litre mixture is 4:3, respectively. 25% of this mixture is taken out and then ____ litres of water is added. This way the final quantity of water in the mixture becomes ____ than the quantity of milk in it. The values given in which of the following options will fill the blanks in the same order in which it is given to make the statement true: I. 140, 15, 10% less II. 196, 12, (75/7)% less III. 224, 44, (125/6)% more IV. 280, 20, (25/3)% less

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.