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*).

#### Solution

(i) The number of articles is directly related to the price. Therefore, they will vary directly with each other.

(ii) The number of articles is directly related to the weight of the articles. Therefore, they will vary directly with each other.

(iii) Speed is constant. Therefore, distance and time does not vary directly.

(iv) The number of hours is directly related to the wages. Therefore, it is a direct variation.

(v) Distance is constant. Therefore, speed and time does not vary directly.

(vi) If the area of a land is large, its cost will also be high. Thus, it is a direct variation.

Thus, the respective values in (i), (ii), (iv) and (vi) vary directly with each other.