Question

Question 61

In questions 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 whitewashing 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.

Answer 1

(i) The number of students in a hostel and consumption of food are directly proportional to each other.
e.g. Let 200 students in a hostel can consume 100 kg of rice in a month.
Then, 400 students in a hostel can consume 200 kg of rice in a month.
(ii) Area of the walls of a room and the cost of whitewashing the walls are directly proportional to each other.
e.g. Let Rs 1000 required for whitewashing a room with $(12\times 8)$ m size.
Then, Rs 2000 required for whitewashing a room with $(12\times 16)$ m size.
(iii) The number of people working and the quantity of work are directly proportional to each other.
e.g. Let 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 =Rs 1000, R =10% and T=1 yr
$\therefore SI=\frac{P\times R\times T}{100}=\frac{1000\times 10\times 1}{100}=Rs100$
But if P =1000, R =20% and T =1yr
$\therefore SI=\frac{P\times R\times T}{100}=\frac{1000\times 20\times 1}{100}=Rs200$
(v) Compound interest on a given sum and the sum invested depends directly nor inversely.