A garrison had provision 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 ?

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
$$\begin{array}{rl}& \therefore x\left(y-10\right)=\frac{4x}{5}\times y\\ & \iff 5xy-50x=4xy\\ & \iff xy-50x=0\\ & \iff x\left(y-50\right)=0\\ & \iff y-50=0\\ & \iff y=50\end{array}$$