a garrison had provisions for a certain number of days after..., Chain Rule, General Mathematics

Question:A garrison had provisions for a certain number of days. After `10` days `1/5`th 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

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+ AnswerD

+ ExplanationInitially, let there be `x` men having food for `y` days.

After `10` days, `x` men had food for `(y - 10)` days.

i.e. `(x - x/5)` or 

`(4x)/5` men had food for `y` days.

`:. x (y - 10) = ((4x)/5)y` or

`xy - 50x = 0` or

`x (y - 50) = 0`. 

So, `y = 50  [ :. x != 0]`

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