Question

The food stocks in a hostel are sufficient for 1200 students for 20 days. If 400 more students joined the hostel, the stock just for ______ days.

Answer 1

Hint: Assume the food stock is sufficient for $$x$$ days. We are given that for 1200 students food stock will enough for 20 days and when 400 students joined afterwards then the number of students will become 1600 so we can apply the direct formula of $$M_1{D}_1=M_2{D}_2$$ where $$M$$ represents the number of students and $$D$$ represents the number of days.

Complete step-by-step solution:
Consider the given information that the food stock is sufficient for 1200 students for 20 days.
Assume that the food stock is sufficient for $$x$$ days.
We have to find the value of $$x$$.
We are given,
$$M_1=1200$$ and $$D_1=20$$
Now, the number of students has been increased by adding 400 students in 1200 students.
Thus, we get,
$$1200+400=1600$$
Hence, the number of students is now 1600
Thus, $$M_2=1600$$
And we have already assumed that the number of days is $$x$$.
So, $$D_2=x$$
Next, we will apply the formula $$M_1{D}_1=M_2{D}_2$$ to find the value of $$x$$
Thus, we get,
$$\begin{gathered} 1200\times 20=1600\times x \\ x={\displaystyle \frac{1200\times 20}{1600}} \\ x=15 \end{gathered}$$
Thus, from this we get that after adding the number of students the number of days gets decreased.
Therefore, the food stock is now sufficient for 15 days.

Note: As the number of students gets increased, it is obvious that the number of days till the food stock will last will be decreased. To find the new total number of students, add the students in the previous no of students to find the total number of students.