Question

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 ??

Answer 1

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

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

$\rule{315}{2}$

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

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

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

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

$\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}$

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

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

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