Answer : Option C

Explanation :

ATQ, 25 people left the fort after 10 days, but still, the remaining food will be consumed at the same rate.
That means if the 150 boys continue till the end, then the remaining food would last for 150 boys for (45-10) = 35 days.
Now After 10 days the remaining food will be (boys * days) 150 * 35 = 5250 unit
But the 25 boys left the for after 10 days
i.e., 125 boys will consume the 5250 unit food in x days
Now, x = 5250/125 = 42 days.
That means the remaining food will last for 42 days.

Solution 2:
The remaining food would last for 150 boys for (45-10) = 35 days. But as 25 boys have gone out, the remaining food would last for a long period (x).
The number of boys and consumption of food are inversely proportional to each other.
That means, 125 boys: 150 boys = 35 days: x
Or, x = (150*35)/ 125 = 42 days
Hence, 125 boys require 42 days to consume the remaining food.