A camp of soldiers has food for 400 days. After 40 days, 150 soldiers leave the camp. As a result. the food can last for 480 days from then onwards. What was the initial number of soldiers?

Let's assume the initial number of soldiers is 'y'.

A camp of soldiers has food for 400 days. After 40 days, 150 soldiers leave the camp. As a result. the food can last for 480 days from then onwards.

$$400\times\ y\ =\ 40\times\ y+480\left(y-150\right)$$

$$10\times\ y\ =\ \ y+12\left(y-150\right)$$

$$10y\ =\ \ y+12y-1800$$

$$13y-10y\ =\ 1800$$

$$3y\ =\ 1800$$

y = 600
So the initial number of soldiers is 600.