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In a garrison of 30 men there was food provision for 10 days if 20 more men arrived then find the no. of days the food will last ?

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Answered by ExploringMathematics
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\textrm{Given : In a garrison of 30 men there was food provision for 10 days}

\textrm{To find : The number of days the food will last if 20 more men arrived}

\rule{315}{2}

\bullet\:\:\textrm{Number of men and number of days food last are inversely proportional}

\textrm{If number of men increases then number of days food last will decrease}

\textrm{and if number of men decreases then number of days food last will increase}

\bullet\:\:\textrm{Initially there are 30 men and food provision was for 10 days.}

\textrm{For 30 men food lasts for 10 days. So, for 1 men food last will for : 30 $\times$ 10 = 300 Days }\textrm{Now if 20 more men arrived then total number of men will be : 30 + 20 = 50}

\textrm{Since for 1 men food last for 300 days}

\textrm{Therefore, for 50 men the number of days food will last : 300/50 = 6}

\boxed{\boxed{\textrm{Hence, if 20 more men arrived, then food will last for 6 days}}}

Answered by Anonymous
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