12.- An army of 900 men has food for 20 days; if you want the provisions to last 10 days Plus, how many men will have to be discharged? 13.- You want to plant trees arranged in 30 rows, so that each row has 24 of them. If they are placed the same trees in 18 rows, how many will there be per row?
12. To find out how many men need to be discharged for the provisions to last 10 days longer, we need to calculate the rate of consumption first.
The total amount of food available is given as enough for 900 men for 20 days. So, the rate of consumption per day for 900 men is:
900 men / 20 days = 45 men per day
To make the provisions last for an additional 10 days, we need to find the total number of men that can be supported for 30 days (20 days + 10 days).
This can be found by multiplying the rate of consumption per day by the desired number of days:
45 men per day * 30 days = 1350 men
Therefore, to make the provisions last for 30 days, an additional 450 men (1350 men - 900 men) will have to be discharged.
13. If you want to place the same number of trees in 18 rows, you need to divide the total number of trees by the number of rows:
Total number of trees: 30 rows * 24 trees per row = 720 trees
Number of trees per row in 18 rows: 720 trees / 18 rows = 40 trees per row
Therefore, there will be 40 trees per row if they are arranged in 18 rows.
12. To calculate the number of men that need to be discharged, we can use the concept of ratios.
First, let's calculate the initial food consumption rate for the army. This can be found by dividing the number of men by the number of days the food will last:
900 men / 20 days = 45 men per day
Next, let's calculate the new number of days the food should last, which is 10 days more than the initial 20 days:
20 days + 10 days = 30 days
Now, we can calculate the number of men that can be supported by the remaining food for 30 days. Since the food consumption rate is 45 men per day, the total number of men that can be supported is:
30 days * 45 men per day = 1350 men
To find the number of men that need to be discharged, subtract the original number of men (900) from the number of men that can be supported (1350):
1350 men - 900 men = 450 men
Therefore, 450 men need to be discharged in order for the provisions to last an additional 10 days.
13. Let's calculate the number of trees required to plant in the 30 rows, assuming each row should have 24 trees.
The total number of trees in the 30 rows can be calculated by multiplying the number of trees per row (24) by the number of rows (30):
24 trees per row * 30 rows = 720 trees
Now, we need to find the number of trees per row for 18 rows.
To do this, we can divide the total number of trees (720) by the number of rows (18):
720 trees / 18 rows = 40 trees per row
Therefore, there should be 40 trees per row if the same number of trees is distributed across 18 rows.