Question

There are 100 students in a hostel. Food provision for them is for 20 days. How long will these provisions last, if 25 more students join the group?​

Answer 1

There are 100 students in a hostel. Food provision for them is for 20 days. How long will these provisions last, if 25 more students join the group?

Suppose the provisions last for y days when the number of students is 125.

We have the following table;

$\sf \boxed{\sf{Number~of~students → 100~and~125}}$

$\sf \boxed{\sf{Number~of~days → 20~and~y}}$

Note that more the number of students, the sooner would the provisions exhaust. Therefore, this is a case of inverse proportion.

So,

100 × 20 = 125 × y

$\sf \frac{100 \times 20}{125}$ = y or 16 = y

Thus, the provisions will last for 16 days, if 25 more students join the hostel.

Alternately, we can write $\sf{ x_1 \: : \: y_1 = x_2 \: : \: y_2}$ as $\sf \frac{x_1}{x_2}$ = $\sf \frac{y_2}{y_1}$.

That is, $\sf{x_1 : x_2 = y_2 : y_1}$

$\Rightarrow$ 100 : 125 = y : 20

$\sf \: y = \frac{100 \times 20}{125} = 16$

Hope this helps uh* :)