A garrison had provisions 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
Answer
Answer (as printed): D
Explanation
Initially, let there be $x$ men having food for $y$ days. After 10 days, $x$ men had food for $(y-10)$ days. Also, $\left(x - \frac{x}{5}\right) = \frac{4x}{5}$ men had food for $y$ days. $\therefore x(y-10) = \frac{4x}{5} \times y \Leftrightarrow 5xy - 50x = 4xy \Leftrightarrow xy - 50x = 0 \Leftrightarrow x(y-50) = 0 \Leftrightarrow y-50 = 0 \Leftrightarrow y = 50$.
Explanation as extracted from the printed page; notation may be imperfect.