Which of the following vary directly and which vary inversely with each other and which are neither of the two?

(i) Number of students in a hostel and consumption of food.

(ii) Area of the walls of a room and the cost of white washing the walls.

(iii) The number of people working and the quantity of work.

(iv) Simple interest on a given sum and the rate of interest.

(v) Compound interest on a given sum and the sum invested.

(i): Number of students in a hostel and consumption of food are direct proportional to each other.

e.g. if 200 students in a hostel can consume 100kg of rice in a month. Then, 400 students in hostel can consume 200kg of rice in a month.

(ii): Area of the walls of a room and the cost of white washing

the walls are directly proportional to each other.

e.g. if ₹ 1000 required for white washing a room with

(12× 8) m size. Then, ₹ 2000 is required to white wash a

room with (12× 16) m size.

(iii): The number of people working and the quantity of work

are directly proportional to each other.

e.g. If 20 workers can complete 20 of a work. Then, 40 workers can complete 40 of the same work.

(iv): Simple interest on a given sum and the rate of interest

are directly proportional to each other.

e.g. Let p = R = 10% and T = 1yr.

∴

But if P = ₹ 1000, R = 20 and T = 1yr.

∴

(v): Compound interest on a given sum and the sum invested are neither depend directly nor inversely.