In a camp of persons there was a provision of food for 42 days. After 10 days the number of persons increased by 300 as a result of which the food lasted only 24 days. What was the number of persons in the camp, originally ?

The correct answer is (b).

Let $x$ be the number of persons in the camp originally. After 10 days, the number of persons is $x+300$. The food lasts for 24 days, so the total amount of food is $24(x+300)$. The food was originally enough for 42 days, so the total amount of food is $42x$. We have the equation $24(x+300)=42x$. Solving for $x$, we get $x=375$.

Option (a) is incorrect because 100 people would have food for 42 days, but after 10 days, there would still be food for 32 days. Option (c) is incorrect because 900 people would have food for 42 days, but after 10 days, there would still be food for 22 days. Option (d) is incorrect because 500 people would have food for 42 days, but after 10 days, there would still be food for 12 days.