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Inverse Proportion

Two quantities may change in such a manner that if one quantity increases, the other quantity decreases. For example as the number of copies of xerox increases, the cost decreases. Similarly the number of workers increases, time taken to finish the job decreases.

Let us look into the following situation
 

Sachin can go to his office in four different ways. He can walk, run, cycle or go by car. Study the following table
 

 

Walking

Running

Cycling

By car

Speed (km/m)

2

4

6

30

Time taken (in min)

30

15

10

2


From the table as the speed increases, time taken to cover the distance decreases.

As Sachin doubles his speed by running, time reduces to half. As he increases his speed to 3 times by cycling, time decreases to one third. Similarly as he increases his speed to 15 times the time taken decreases to one fifteenth.
So from the above example if we increase the speed time taken decreases. It is a inverse proportion.

 

Example

5 tankers are required to fill a tank in 2 hours 30 minutes. How long will it take if only 3 tankers of the same type are used?
 

Number of tankers

5

3

Time (in minutes)

150

x

 

Solution

Lesser the number of tankers, more will be time required by it to fill the tank. So this is a inverse proportion.


Time taken to fill the tank by 3 tanks is 4hrs 16 minutes.

 

Example

There are 30 students in a class. The number of table required for them is 18. If 15 of them are added to this class how many tables will be needed?

Number of students

30

45

Number of tables

18

?

Solution

As the number of students increases number of tables required for the class also increases. This is a direct proportion.

Number of tables required = 27.

 

Example

If 10 workers clear the tank in 24 hours. How many workers will be required to do the same work same work in 12 hours.

Number of hours

24

12

Number of workers

10

x

 

Solution

As the time decreases, number of workers involved in that work increases. This is an inverse proportion.

20 workers are need to complete the same work in 12 hrs





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