When one quantity increases, the other quantity also increases

Like,

     If distance increases, time taken also increases

     If number of books purchased increases, total cost also increases

 

So, we can say that

          Distance and Time are directly proportional

Similarly,

  Number of books purchased and cost are directly proportional

 

How to solve questions with Direct Proportion?

Let’s take an example

 

Suppose it takes us 1 hour to drive 50 km. How many hours would it take to drive 200 km?

 

Given that,

It takes 1 hour to drive 50 km

We need to find how  many hours would it take to drive 200 km

 

Let the time taken to drive 200 km be x hours

 

Now, we draw a table

Time (in hours) 1 x
Distance (in km) 50 200

 

Now, as distance increases,

time taken will also increase

So, Time and Distance are in direct proportion

 

So, we write numbers as

1.jpg

 

So, 

      x 1 /  y 1  = x 2 /y 2

          1/50=x/200

  1/50  × 200 = x

     1/5  × 20 = x

                4 = x

                x = 4

 

So, it takes 4 hours to travel 200 km

 

Let’s take another example

 

Suppose we have brought 10 books for Rs 1000. How much is the price of 45 books?

 

Given that,

Cost of 10 books is Rs 1000

We need to find price of 45 books

 

Let cost of 45 books be Rs y

 

Now, we draw a table

Time (in hours) 10 45
Distance (in km) 1000 y

 

Now, as number of books increases,

cost of books will also increase

So, they are in direct proportion

 

So, we write numbers as

  x 1 /y 1  = x /y 2

  10/1000=45/y

  10 × y =   45 × 1000

   y = 1/10 × 45 × 1000

   y = 45 × 100

   y = 4500

So, 45 books will cost Rs 4500

  1. Chapter 13 Class 8 Direct and Inverse Proportions
  2. Concept wise

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.