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During a wartime, a group of $$n$$ soldiers had enough food to last for 30 days. After 10 days, 50 more soldiers joined. If the food now can only last for 16 days, the value of $$n$$ is
After 10 days the remaining food would have fed the original $$n$$ soldiers for 20 more days, which is $$20n$$ soldier-days. With $$n + 50$$ soldiers it lasts 16 days, so $$20n = 16(n + 50)$$. This gives $$4n = 800$$ and $$n = 200$$.
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