In a hostel mess there are food supplies for 40 boys to last 30 days. After 9 days, some boys left the hostel. The food supplies ran out after 44 days from the beginning. How many boys left the hostel?

Question: In a hostel mess there are food supplies for 40 boys to last 30 days. After 9 days, some boys left the hostel. The food supplies ran out after 44 days from the beginning. How many boys left the hostel?

Solution:
First, let's find out how much food was remaining after 9 days.
Total boys = 40
Initial food supply = 30 days
After 9 days, remaining food would last = 30 - 9 = 21 days (for 40 boys)

According to the question, the total food lasted for 44 days from the beginning.
Since the boys left after 9 days, the remaining food lasted for = 44 - 9 = 35 days.

Now,
Food for 21 days is sufficient for = 40 boys
Food for 1 day is sufficient for = 40 × 21 boys
Food for 35 days is sufficient for = (40 × 21)/35 boys
= 24 boys

So, the number of boys remaining in the hostel is 24.
Number of boys who left = 40 - 24 = 16

∴ The number of boys who left the hostel is 16.