Question

there are 1000 students in a hostel food provision for them is for 20 days. how long will these provision last if 250 more students join the group ​

Answer 1

Step-by-step explanation:

The amount of provisions (call this p) required is directly proportional to the number of students (call this n) and the number of days (call this t) in the hostel.

Mathematically, p ∝ nt or

p=knt (k being a constant for provisions per student-day)

Then p1 = kn1t1 (for 1st situation with 100 st for 20 d) and

p2 = kn2t2 (for 2nd situation with 125 st for an unknown number of days, t2)

Note that the k is the same for both situations because it is assumed that both groups need the same amount of provisions/student-day and

p1 = p2 because the group of 100 students (n1) for 20 days (t1) will have the same amount of provisions as the group of 100 students (n2) for t2 days (the question you are asking for a solution). Therefore,

kn1t1 = kn2t2 or

n1t1 = n2t2 (constants k cancel each other out)

Isolating the variable t2 algebraically,

t2 = n1t1/n2 or

t2 = (100 students)(20 days)/125 students

t2 = 16 days (Final answer)