Direct and Inverse Proportions
NCERT Exercise and Other Q & A
If there is an increase (↑) [decrease (↓)] in one quantity produces a proportionate decrease (↓) [increase (↑)] in another quantity, then we say that the two quantities are in inverse variation or inverse proportion.
If two quantities vary inversely, their product is a constant.
e.g. if and y are two quantities which are in inverse proportion then,
x × y = constant
or x1 × y1 = x2 × y2
NCERT Exercise 13.2
Q1: Which of the following are in inverse proportion?
(i) The number of workers on a job and the time to complete the job.
(ii) The time taken for a journey and the distance travelled in a uniform speed.
(iii) Area of cultivated land and the crop harvested.
(iv) The time taken for a fixed journey and the speed of the vehicle.
(v) The population of a country and the area of land per person.
Answer:
(i) With an increase in number of workers, the job will complete in lesser time. ∴ The number of workers on a job and the time to complete the job are in inverse proportion.
(ii) At constant (uniform) speed, more time means more distance will be covered. ∴ The time taken for a journey and the distance travelled in a uniform speed are in direct proportion.
(iii) An increase (↑) in the cultivated area means an increase (↑) in the crop harvested. ∴ Area of cultivated land and the crop harvested are in direct proportion.
(iv) An increase (↑) in speed of the vehicle means the distance will be covered in lesser (↓) time. ∴ The time taken for a fixed journey and the speed of the vehicle. are in inverse proportion.