Answer:
The food will last for 20 days
Explanation:
The equation of the inverse proportional is xy = k, where k is the constant of variation
∵ In a hostel of 40 students, there is food for 30 days
→ That means the food is the constant k and the number of days y
varies inversely with the number of students x
∴ x = 40 and y = 30
∵ xy = k
∴ 40 × 30 = k
∴ 1200 = k
∴ The equation of the inverse proportional is xy = 1200
∵ 20 more students join the hostel
→ That means the number of students increased by 20
∴ The number of students in the hostel = 40 + 20
∴ The number of students in the hostel = 60
→ By using the equation above
∵ 60 × y = 1200
∴ 60y = 1200
→ Divide both sides by 60
∴ y = 20
∴ The food will last for 20 days