Question

1500 soldiers in a fort have provision for 48 days.After 13 days few soldiers join them and the food lasts 25 days how many soldiers join

Answer 1

Answer: This is a problem of inverse variation, where the number of days that the food lasts is inversely proportional to the number of soldiers in the fort. We can use the formula:

d = k / s

where d is the number of days, s is the number of soldiers, and k is a constant of proportionality. We can find the value of k by using the initial information:

48 = k / 1500 k = 48 * 1500 k = 72000

Now we can use the information after 13 days to find the new number of soldiers. Let x be the number of soldiers who joined the fort. Then we have:

25 = 72000 / (1500 + x) 25 * (1500 + x) = 72000 37500 + 25x = 72000 25x = 34500 x = 1380

Answer: The number of soldiers who joined the fort after 13 days is 1380.

Answer 2

600 soldiers

Step-by-step Explanation:

Let's assume that the number of soldiers who joined the fort after 13 days is x.

After 13 days, the total number of soldiers in the fort is 1500 + x.

We know that the food in the fort lasts for 25 days after 13 days.

This means that the total number of days of food left after 13 days is 25 × (1500 + x).

We also know that the total number of days of food available is 1500 × 48 = 72,000.

Therefore, we can set up the following equation:

`\sf 72,000 - 1500 * 13 = 25 * (1500 + x)`

`\sf 52500 = 25 * (1500 + x)`

Divide both sides by 25.

`\sf (52500)/(25) = (25 * (1500 + x) )/(25)`

`\sf 2,100 = (1500+x)`

Subtract 1500 on both sides:

`\sf 2,100 -1500= 1500+x-1500`

Solving for x, we get:

x = 600

Therefore, 600 soldiers joined the fort after 13 days.