Which of the following quantities vary directly with each other? (i) Number of articles (x) and their price (y). (ii) Weight of articles (x) and their cost (y). (iii) Distance x and time y, speed remaining the same. (iv) Wages (y) and number of hours (x) of work. (v) Speed (x) and time (y) (distance covered remaining the same) (vi) Area of a land (x) and its cost (y).

Explanation

(i) Number of articles (`x`) and their price (`y`).
If number of articles is increasing then cost will also increase.
So, it is a case of directly proportion.

(ii) Weight of articles (`x`) and their cost (`y`).
When weight of the article is increasing then cost also increase.
So, it is a case of directly proportion.

(iii) Distance `x` and time `y`, speed remaining the same.
Time increases when distance increases, if speed remains constant.
So, it is a case of directly proportion.

(iv) Wages (`y`) and number of hours (`x`) of work.
Wages increases if the number of working hours increases.
So, it is a case of directly proportion.

(v) Speed (`x`) and time (`y`) (distance covered remaining the same).
For same distance time taken will reduce if speed is increased.
So, it is not a case of directly proportion.

(vi) Area of a land (`x`) and its cost (`y`).
Cost of the land increases if its area increases.
So, it is a case of directly proportion.