Question

The hostel of a college having 320 students has a stock of food for 80 days. If 20 students leave the hostel after 20 days, for how many more days will the food last?

Answer 1

Hint:
First, we will multiply the total number of student with the availability of the stock and then with the consumption of food. Then, we will find the number of days when food is left for each student by subtracting the food used in 20 days from food for each student. After calculating the number of students left, we will divide the food left by it to find the number of the day the food will last.

Complete step by step solution:
We are given that the number of students is 320 and food stock for 80 days.
Multiplying 320 by 80 to find the availability of food per student, we get
\[
  {\text{Food available per student }} = 320 \times 80 \\
   = 25600{\text{ days}} \\
 \]
Now we will find the food consumed in 20 days.
\[
  {\text{Food consumed in 20 days }} = 320 \times 20 \\
   = 6400 \\
 \]
Then we will find the number of days when food is left for each student.
\[
  {\text{Food left for each student = Food for each student }} - {\text{ Food used in 20 days}} \\
   = 25600 - 6400 \\
   = 19200 \\
 \]
Subtracting 20 students from the total number of students, we get
\[
  {\text{Number of students left}} = 320 - 20 \\
   = 300 \\
 \]
We know that we have the case of indirect proportion as the number of men will decrease food will last for a greater number of days.
Dividing the food left for each student by the number of students left, we get
\[
  {\text{Food would last for days}} = \dfrac{{{\text{Food left for each student}}}}{{{\text{Number of students left}}}} \\
   = \dfrac{{19200}}{{300}} \\
   = 64{\text{ days}} \\
 \]

Therefore, it will take 64 more days that food would last.

Note:
In these types of questions, students have to keep in mind the concept of inverse proportion that when one value decrease than the other value increases at the same rate. Similarly, as the number of men will decrease, food will last for a greater number of days. Also, do the comparisons very carefully. Students have to read the question properly and then try to solve the question step by step, which will reduce the confusion.