Question

100 persons have food provision for 4 days. If 20 persons left the place, the provision will last for
A) 30 days
B) 5 days
C) 120 days
D) 40 days

Answer 1

Hint: We have been given the number of persons and their food provision, using this, we can find the total amount of food available. Then when 20 people leave, the food requirement would change. So, the number of days for the food to last will be given by the division of total food available with the new requirement.

Complete step-by-step answer:
It is given that for 100 persons (P), the food provision was for 4 days (n). Let the amount of food consumed per day be x.
🡪 P = 100 and n = 4
The total food available (F) will be equal to the product of total persons (P), number of days (n) and the food consumed per day (x)
 $$\begin{gathered} \Rightarrow F=P\times n\times x \\ \Rightarrow F=4\times 100\times x \\ \to F=400x \end{gathered}$$
Now, 20 people out of 100 left. The number of people remaining will be:
 $100-20=80$
The new food requirement will be its product with food consumption per day
 $f=80x$
So, the total number of days food will last (N) will be equal to the total food available divided by the new food requirement
 $N={\displaystyle \frac{F}{f}}$
Substituting the values, we get:
 $$\begin{gathered} \Rightarrow N={\displaystyle \frac{400x}{80x}} \\ \Rightarrow N=5 \end{gathered}$$
Therefore, if 20 people leave the place, the provision will last for 5 days.
So, the correct answer is “Option B”.

Note: This is the case of inverse proportionality, we can check the answer through this as well.
When there are more people the food will last for less number of days and vice – versa. So when the people are reduced here from 100 to 80, the food should have lasted for more than 4 days.