Unit Rate Formula

Generally, a rate specifies the ratio that compares the two different quantities of different units. Example:- Kilometer per Hour (kmph), Miles per Hour (mph), etc. The word per indicates that we are dealing with the rate concept. The term per can be represented symbolically as “/”. The current topic Unit Rate also comes under the rate topic as discussed above. 

Unit Rate Formula 

It can be defined as the ratio between two different measurements in which the second quantity or term is equal to 1 i.e., a certain number of units of the first quantity is compared to the one unit of the second quantity. Unit Rate formula has denominator 1. Suppose an example for the unit rate is there are 60 minutes in one hour. So unit rate can express be like 60 minutes per one (1) hour. Unit Rate formula for the two quantities/measurements A, B is given  by,

Unit Rate = Ratio between two different measurements of different units

= A:B

= A/B

Let’s look into a few problems on Unit Rate to get a better understanding.

Sample Questions

Question 1: If a shopkeeper gave 10 pencils to a student at a cost of 45 rupees then what is the unit cost?

Solution:

Given,

Cost of pencils student bought (A) = 45

Count of pencils (B) = 10

Unit Cost of pencil = Cost of all pencils/Count of pencils

= 45/10

= 4.5/1

So per unit cost of pencil is 4.5 rupee.

Question 2: A bike rider travel 200 km in 4hours. Apply unit rate formula to find how much distance he travels in one hour.

Solution:

Given,

Distance travelled by rider (A) = 200Km

Time taken to travel (B) = 4 hours

Unit rate Formula = Distance travelled by rider/time taken to travel

= 200/4

= 50/1

So per unit hour the rider travel 50 km. i.e., 50kmph

Question 3: In a Bookstall, Seller offers a dozen plain notebooks at a cost of 360 rupees. Find the cost of each unit?

Solution:

Given,

Cost of total books = 360 rupees

Number of books = 12

Unit rate Formula = Cost of total books/Number of books

= 360/12

= 30/1

Hence unit cost of a book is 30 rs.

Question 4: A paperboy delivers 183 newspapers in 3 hours in the early morning daily. How many papers will the paperboy distribute in an hour?

Solution:

Number of news papers distributed by a paperboy = 183

Time taken to distribute papers = 3 hours

Unit Rate formula to determine how may news paper a paper distribute in an hour is

= Number of news papers distributed/Time taken

= 183/3

= 61/1

So per unit hour a paperboy can distribute 61 newspapers. 

Question 5: A car driver traveled 65km per hour on a highway. How much distance will the driver travel in a day?

Solution:

Given,

Distance travelled by a driver in an hour = 65km

A day has 24 hours, so Distance travelled by a driver in 1 day = 65 × 24

= 1560km

Unit rate representation of distance travelled per day = 1560/1

Question 6: Suppose there are 50 flats in an apartment containing 5 floors. How many flats will be present on a floor? (Hint- Use unit rate formula)

Solution:

Given,

Number of flats = 50

Number of floors = 5

Number of flat in each floor = Number of flats/Number of floors

= 50/5

= 10/1

Number of flat per unit floor = 10