In a fort, 150 men had provisions for 45 days. After 10 days, 25 men left the fort. How long would the food last at the same rate?

Original no. of men in the fort = 150

New no. of men in the fort = 150 - 25 = 125

For 125 men lets take food will last for x days.

The remaining food would last (45 - 10) = 35 days

Since it is a case of inverse variation,

$\therefore 150 \times 35 = 125 \times x\\[1em] \Rightarrow 5,250 = 125x\\[1em] \Rightarrow x = \dfrac{5,250}{125}\\[1em] \Rightarrow x = 42$

Hence, the food last for 42 days.