Question

In a hostel of 50 girls, there are food provisions for 40 days. If 30 more girls join the hostel, how long will these provisions last?

Answer 1

$$\text{ Let x be the number of days with food provisions for 80 (i . e . , 50 + 30) girls }.$$

Number of girls	50	80
Number of days	40	x

$$\text{ Since the number of girls and the number of days with food provisions are in inverse variation, we have: }$$
$$50\times 40=80x$$
$$\Rightarrow x=\frac{50\times 40}{80}$$
$$=\frac{2000}{80}$$
$$=25$$
$$\text{ Thus, the required number of days is }25.$$