Question

Ration is available for $100$ students in a hostel for $40$ days. How long will it be last, if $20$ more students join in the hostel after $4$ days?

Answer 1

As the number of students increase, ration will last for less number of days in the same proportion are in inverse proportion
No. of days No. of students
ration available
$40$ $100$
After 4 days $36$ $100$
$x$ $120$
Now the question is if there is availability of rice for $36$ days for $100$ students
How long will it last for $120$ students.
$\frac{36}{x}=\frac{120}{100}$
$x=\frac{36\times 100}{120}=30$ days (Since the number of students are increasing $100\times x=120\Rightarrow x=\frac{12}{100}$ so the no. of days will decrease in same proportion)