Concept of Rate

Before defining rate, first we consider some examples.

1. If one dozen eggs cost 24 Rs., what is the cost of 1 egg?

(Ans). One dozen eggs cost = 24 Rs
            Cost of 1 egg = 24/12=2Rs/egg

2. A car travels 540 km consumed 60 liters petrol. Find distance travelled in liter.

(Ans). In 60 liters distance travelled= 540km
            In 1 liter distance travelled = 540/60=9km/liter

3. A boy works 5-hour and paid 120 Rs. Find his pay for one hour.

(Ans) In 5 hours boy gets = 120 Rs.
            In 1 hour boy gets = 120/5=24Rs/hour

In each of the above examples, the two quantities that is the quantity in numerator and the quantity in denominator have different units, whereas in ratio both quantities have same units.

The division of two quantities having different unit, is called RATE
In the above examples, we have

  1. Rate = 24/12 = 2Rs/egg
  2. Rate = 540/60 = 9km/liter
  3. Rate = 120/5 = 24Rs/hour

Example:
A car uses 40 liters of petrol to travel 320 km. How far can is travel for 32 liters?
Solution:
In 40 liters car traveled = 320km
In 1 liter car traveled = 320/40 = 6km/liter
In 32 liter car traveled = (8km/liter)(32liter) = 256km