# Which of the following is in direct proportion

(a) One side of a cuboid and its volume

(b) Speed of a vehicle and the distance travelled in a fixed time interval

(c) Change in weight and height among individuals

(d) Number of pipes to fill a tank and the time required to fill the same tank

**Solution:**

Direct proportion means that if one variable increases the other also increases in some proportion.

(a) One side of a cuboid and its volume.

The volume of a cuboid is = V = L × B × H ( L = length; B = Breadth; H = height). So if one side of the cuboid increases the volume of the cuboid may increase or decrease depending on whether the other sides increase or decrease. So it may happen that the length of one side might decrease but other sides may be increased to increase the volume.

(b) Speed of a vehicle and the distance travelled in a fixed time interval.

In a fixed time interval as the speed of the vehicle increases the distance covered is more. Hence the speed of the vehicle and the distance travelled in a fixed time interval are directly proportional

(c) Change in height and weight among individuals

As the height of the individual increases the weight may increase or decrease. The weight of the individual just not depends on the height but other factors. Hence the height of the individual and weight of the individual are not necessarily directly proportional.

(d) Number of pipes used to fill a tank and the time required to fill the tank

As the number of pipes to the tank increases the faster the tank fills up. Hence we can say that the number of pipes and the time required to fill the tank are inversely proportional. As the number of pipes increases the time taken to fill the tank decreases.

Hence only (b) is in direct proportion.

**✦ Try This: **Which of the following is in direct proportion?

(a) Length of one side of a square and its area.

(b) Time taken to cover distance if the speed of a vehicle is fixed.

(c) Amount of gasoline in the fuel tank of a car and distance covered.

(d) Number of workers employed and time taken to complete a given work.

(a) Length of one side of a square and its area

If the side of the square is of the length s then the area of the square is s². Therefore as the length of the side increases the area of the square increases. Hence length of the side of the square and the area of the square are directly proportional.

(b) Time taken to cover distance if the speed of the vehicle is fixed.

If the speed of the vehicle is fixed then the time taken to cover a distance will increase as the distance increases. Hence as the distance increases time taken also increases.

(c) Amount of gasoline in the fuel tank of a car and distance covered.

The more the gasoline we have in the tank the longer the distance we can cover. Hence there is a direct proportion between gasoline in the tank and distance covered.

(d) Number of workers employed and time taken to complete a given work.

To finish a given amount of work early we will keep more workers. Hence the number of workers and time to finish a given work are inversely proportional and not directly proportional.

(a), (b) and (c ) are in direct proportion.

**☛ Also Check: **NCERT Solutions for Class 8 Maths Chapter 13

**NCERT Exemplar Class 8 Maths Chapter 10 Sample Problem 3**

## Which of the following is in direct proportion (a) One side of a cuboid and its volume, (b) Speed of a vehicle and the distance travelled in a fixed time interval, (c) Change in weight and height among individuals, (d) Number of pipes to fill a tank and the time required to fill the same tank

**Summary:**

The following relations are in direct proportion: (a) One side of a cuboid and its volume, (b) Speed of a vehicle and the distance travelled in a fixed time interval, (c) Change in weight and height among individuals

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