A garrison of ‘n’ men had enough food to last for 30 days. After 10 days, 50 more men joined them. If the food now lasted for 16 days, what is the value of n?

Question: A garrison of ‘n’ men had enough food to last for 30 days. After 10 days, 50 more men joined them. If the food now lasted for 16 days, what is the value of n?

Solution:
After 10 days, the food for n men is there for 20 days.
This food can be eaten by (n + 50) men in 16 days.

So,
20n = 16(n + 50)
⇒ 20n - 16n = 800
⇒ 4n = 800
∴n = 200