Types of Variation

Two quantities are said to have direct variation if, when one quantity increases, the other quantity also increases, and when one quantity decreases, the other quantity also decreases.

Two quantities are in inverse variation if, when one quantity increases, the other decreases, and when one decreases, the other increases.

A car, running with uniform speed, covers a distance of 96 km in 3 hours. How much distance will the car cover in 5 hours, running at the same speed?

Solution:
In 3 hours, car covers 96 km

⇒ In 1 hour, car covers

96 In 1 hour, car covers `96/3` km  = 32 km

And, in 5 hours, car covers = 32 km × 5 = 160 km. 

A car can travel 360 km, consuming 24 litres of petrol. How much petrol will it consume while travelling a distance of 480 km?

Solution:
Car can travel 360 km, consuming 24 litres of petrol.

 ⇒ Car can travel 1 km consuming `24/360` litres of petrol.

And the car can travel 480 km, consuming `24/360` × 480 litres of petrol.

                                                                 = 32 litres of petrol 

A car covers a distance of 30 km, consuming 2 litres of petrol, whereas a motorcycle covers a distance of 90 km, consuming 1.2 litres of petrol.

1. How much distance will each cover after consuming 3 litres of petrol?
2. Which of these two will cover more distance (each consuming 3 litres of petrol), and by how much? 

Solution:

(i) Consuming 2 liters of petrol, the car covers 30 km

⇒ Consuming 1 liter of petrol, the car covers `30/2` km = 15km

And, consuming 3 litres of petrol, the car covers 15 km × 3 = 45 km.

Now, consuming 1.2 litres of petrol, the motorcycle covers 90 km.

 ⇒ Consuming 1 liter of petrol, motorcycle covers `90/1.2` km = 75 km.

And, consuming 3 litres of petrol, motorcycle covers 75 × 3 km = 225 km

(ii) Motorcycle covers more distance, by 225 km - 45 km = 180 km 

The number of men and the number of days taken by them to complete certain work. Clearly, if the number of men is more (increased), the number of days taken by them to complete the same work is less (decreased). And, if the number of men is less (decreased), the number of days taken by them to complete the same work is more (increased).

Explanation:

• Inverse Relationship

• More Men → Fewer Days

• Fewer Men → More Days

• Total Work Remains Constant

• Variation: When two things change together

• Direct Variation: Both go up or down together

• Inverse Variation: One goes up, the other goes down

• Constant: Fixed number in a formula