Question
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 ?
Answer: Option D
Initially, Let there be x men having food for y days
After 10 days, x men had food for days (y - 10)
Also, $$\left( {x - \frac{x}{5}} \right)$$ men had food for y days
$$\eqalign{
& \therefore \,x\left( {y - 10} \right) = \frac{{4x}}{5} \times y \cr
& \Leftrightarrow 5xy - 50x = 4xy \cr
& \Leftrightarrow xy - 50x = 0 \cr
& \Leftrightarrow x\left( {y - 50} \right) = 0 \cr
& \Leftrightarrow y - 50 = 0 \cr
& \Leftrightarrow y = 50 \cr} $$
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Initially, Let there be x men having food for y days
After 10 days, x men had food for days (y - 10)
Also, $$\left( {x - \frac{x}{5}} \right)$$ men had food for y days
$$\eqalign{
& \therefore \,x\left( {y - 10} \right) = \frac{{4x}}{5} \times y \cr
& \Leftrightarrow 5xy - 50x = 4xy \cr
& \Leftrightarrow xy - 50x = 0 \cr
& \Leftrightarrow x\left( {y - 50} \right) = 0 \cr
& \Leftrightarrow y - 50 = 0 \cr
& \Leftrightarrow y = 50 \cr} $$
Was this answer helpful ?
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