Question : A camp of soldiers has food for 200 days. After 20 days, 100 more soldiers join the camp and the food now can last for 80 days. What was the initial number of soldiers in the camp?
Option 1: 140
Option 2: 100
Option 3: 120
Option 4: 80
Correct Answer: 80
Solution :
Let's the initial number of soldiers as $x$ and the initial number of days the food could last for 200
Food Supply = the number of soldiers × the number of days = $x×200$
After 20 days, food for (200 – 20) = 180 days remained for $x$ soldiers.
So, $x×180 = (x+100)×80$
⇒ $100x = 800$
⇒ $x = 80$
Hence, the correct answer is 80.
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