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}$

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

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

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

Answer 2

Step-by-step explanation:

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

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