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: We will assume the food stock is sufficient for particular days say ${D_2}$. Since, it is already given in question that food for 1200 students is sufficient for 20 days. We will have to find the number of days for 1600 students as 400 more students joined. We can depict the relation as ${N_1}{D_1} = {N_2}{D_2}$ where $N$ is the number of students and $D$ is the number of days. In this question, food stock is constant. There is a change in food stock and number of students.

Complete step-by-step answer:
The given numbers of students are 1200 and the food stock of 1200 students is enough for 20 days. After 400 students joined, the total number of students became 1600. This can be expressed as:
The numbers of students were ${N_1} = 1200$
The food stock is sufficient for ${D_1} = 20\;{\rm{days}}$
The number of students after 400 students joined ${N_2} = 1200 + 400 = 1600$
We need to find ${D_2}$ the number of days after joining 400 students.
We will use the relation as expressed
${N_1}{D_1} = {N_2}{D_2}$
We will substitute 1200 for ${N_1}$ , 20 days for ${D_1}$ and 1600 for ${N_2}$ .
$\begin{array}{l}
1200 \times 20\;{\rm{days}} = 1600 \times {D_2}\\
{D_2} = \dfrac{{1200 \times 20\;{\rm{days}}}}{{1600}}\\
{D_2} = 15\;{\rm{days}}
\end{array}$
Hence the food stock is sufficient for 15 days after the arrival of 400 more students.

Note: The food stock is constant here. Hence if the number of students increases, we can easily predict that the food stock will be sufficient for fewer days. By 400 more students in question, we mean adding 400 more to 1200, that is now the number of students is 1600.