A king had 45,750 kg of wheat grains in his store house. Total consumption ofpeople is 5790 kg, rest for soldiers. There are 30 soldiers, each soldiers eat 3kgper day. Find the duration for which wheat will last for the soldiers.

Sure, let's break down the problem step by step to find out how long the wheat will last for the soldiers.

1. Total Wheat in Storehouse: The king has a total of 45,750 kg of wheat grains in his storehouse.

2. Wheat Consumed by People: The total consumption of wheat by the people is 5,790 kg.

3. Wheat Remaining for Soldiers: To find out how much wheat is left for the soldiers, we subtract the wheat consumed by the people from the total wheat: $\text{Wheat remaining for soldiers} = 45,750 \, \text{kg} - 5,790 \, \text{kg} = 39,960 \, \text{kg}$

4. Daily Consumption by Each Soldier: Each soldier eats 3 kg of wheat per day.

5. Total Number of Soldiers: There are 30 soldiers.

6. Total Daily Consumption by All Soldiers: To find out the total daily consumption of wheat by all soldiers, we multiply the daily consumption per soldier by the number of soldiers: $\text{Total daily consumption} = 30 \, \text{soldiers} \times 3 \, \text{kg/soldier/day} = 90 \, \text{kg/day}$

7. Duration for Which Wheat Will Last: To find out how many days the wheat will last for the soldiers, we divide the total wheat remaining for the soldiers by the total daily consumption: $\text{Duration} = \frac{39,960 \, \text{kg}}{90 \, \text{kg/day}} = 444 \, \text{days}$

So, the wheat will last for the soldiers for 444 days.