Answer :
The batch proportions for a concrete mixture with a capacity of 400 liters, based on the given mix proportions, are as follows: 75 kg of cement, 39 liters of water, 221 kg of stone, and 145 kg of sand.
To determine the batch proportions, we need to adjust the given mix proportions to the desired capacity of 400 liters. Firstly, we calculate the adjusted mass of stone by considering its moisture content. The dry mass of stone is 1103 kg, and with a moisture content of 1.5%, the actual mass of stone is 1103 kg - (1103 kg * 0.015) = 1086.945 kg.
Next, we calculate the adjusted mass of sand by considering its moisture content. The dry mass of sand is 727 kg, and with a moisture content of 6%, the actual mass of sand is 727 kg - (727 kg * 0.06) = 683.62 kg.
Now, we can determine the batch proportions. The cement content is given as 375 kg, and the water content is given as 195 liters. For a mixture with a capacity of 400 liters, the adjusted batch proportions are as follows: 375 kg * (400 litres / 195 litres) = 76.92 kg of cement, and 195 litres * (400 litres / 195 litres) = 100 litres of water.
Finally, we calculate the proportions of stone and sand. The adjusted mass of stone is 1086.945 kg, and the adjusted mass of sand is 683.62 kg. To maintain the same ratio between stone and sand, we calculate the ratio of adjusted masses: 1086.945 kg / 683.62 kg = 1.59.
Therefore, the batch proportions for a concrete mixture with a capacity of 400 liters are approximately: 76.92 kg of cement, 100 liters of water, 221 kg of stone (1086.945 kg / 1.59), and 145 kg of sand (683.62 kg / 1.59).
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