Question 61

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?

Solution

Let's assume the initial number of soldiers is 'y'.

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.

$$200\ \times\ y\ =\ 20\times\ y+80\left(y+100\right)$$

$$200y\ =\ 20y+80y+8000$$

200y = 100y+8000

200y-100y = 8000

100y = 8000

y = 80

The initial number of soldiers in the camp = 80

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