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The remaining food would last for 150 men for (45  10) = 35 days
Now, 25 men have gone out, the ramaining food would last for a longer period.
Hence, by the rule of three, we have the following relationship.
125 men : 150 men = 35 days : required number of days
∴ required number of days = (150 x 35)/125 = 42 days.
Let the required number of days be a.
Less men → more days.
Thus the two quantities are inversely proportional to each other.
Men 
125 (x_{1}) 
150 (x_{2}) 
Days 
35 (y_{1}) 
a (y_{2}) 
x_{1}y_{1}= x_{2}y_{2}
⇒ 125 x 35 = 150 x a
⇒ a =
125 x 35
/
5
= 3 x 28 = 84 days
