Question

a hostel had rations for 60days for 500students after 12days 300 more students join the hostle how long will the remaining ration last

Answer 1

$r = d \times s$
the total ration is the product of the days and students.
total ration = 60*500 = 30000
in 12 days, the ration completed = 12*500 = 6000
remaining ration = 30000-6000 = 24000
additional students = 300
now, total students = 500+300 = 800
now, to find the number of days the remaining ration will last, we modify the above formula as
$d = r \div s$
d = 24000/800 = 30 days
the remaining ration will last 30 days

Answer 2

After 12 days means 60-12=48 days

300 more students join so 800 students are the present strength

This is a case of inverse variation

So x1.y1=x2.y2

48.500=x2.800

x=30