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Direct and Inverse Proportions - Class 8 : Notes


1. Direct Proportion:
For any ratio x/y, if on changing the values of x & y, the ratio x/y does not change. Then, we say that x and y are in direct proportion.
In other words, one quantity is a constant multiple of the other quantity i.e. if x = ky where k is a constant. Then, we say that x and y are in direct proportion.

ExampleConsider the per hour wages paid a company to its employees.

No. of working hours

Paid Wages (in Rs.)

1

100

2

200

3

300

4

400

5

500

6

600

7

700

8

800

Here, if we consider x as no. of working hours and y as paid wages, then we can find the direct proportion between the two quantities. Moreover, the answer of ratio remains same for each case.
If we consider x = 1 and y =100, we get x/y = 1/100.
Now, we consider x = 7 and y = 700, we get x/y = 7/700 = 1/100.
Thus, in any case ratio x/y will remain constant.

 

2. Inverse Proportion:
For any ratio x/y, if on increasing x by certain amount the quantity y decreases by the same amount. Then, we say that x and y are in inverse proportion.
In other words, if the product of two quantities is constant i.e xy = k where k is constant. Then, we say that x and y are in inverse proportion.

ExampleConsider the speed and time relationship for five trains to travel same distance.

Train No.

Speed (in kmph) Time Taken (in Hrs)

1

25

5

2 50

2.5

3

75

1.67

4 100

1.25

5 125

1

Here, we can see that as the speed increases the time taken to travel decreases.
Let us consider x as speed and y as time taken.
For train 1, x = 25 and y = 5. So, xy = 125.
For train 4, x = 100 and y = 1.25. So, xy = 125.
Thus, in any case product xy will remain constant.



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