Question

14. A garrison have provisions for a certain number of days; after 10 days 1/5 of the men desert and it is found that the provisions will now last just as long as before; how long was that?
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Answer 1

Answer:

50 days

Step-by-step explanation:

Let "x" men have provisions for "y" days.

Then, "x" men have provisions for (y - 10) days.

( x - $\frac{x}{5}$ ) men have provisions for "y" days.

x(y - 10) = $\frac{4x}{5}$ × y

xy - 10x = 0.8xy

x(0.2y - 10) = 0

0.2y - 10 = 0

y = 10 ÷ 0.2

y = 50 days