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1. A garrison had provision for a certain number of days. After 10 days, $\frac{1}{5}$ of the men desert and it is found that the provisions will now last just as long as before. How long was that ?

A. 15 days

B. 25 days

C. 35 days

D. 50 days

Solution:

Initially, Let there be x men having food for y days
After 10 days, x men had food for days (y - 10)
Also,

(x - \frac{x}{5})

men had food for y days

\begin{aligned} ∴ x (y - 10) = \frac{4 x}{5} \times y \\ \Leftrightarrow 5 x y - 50 x = 4 x y \\ \Leftrightarrow x y - 50 x = 0 \\ \Leftrightarrow x (y - 50) = 0 \\ \Leftrightarrow y - 50 = 0 \\ \Leftrightarrow y = 50 \end{aligned}

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