Question

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

• A. 35 days
• B. 15 days
• C. 25 days
• D. 50 days

Answer 1

The correct option is D 50 days

Initially, let x men had provisions for y days.

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

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

Therefore, $x(y-10)=\frac{4x}{5}\times y$

$5xy-50x=4xy$

$xy-50x=0$

$x(y-50)=0$

$y=50$