Direct & Inverse Proportion

 

Variations:

If the value of two objects depends upon each other in such a way that the increase or decrease in the value of one object affects the value of another object then these two objects are said to be in variation.

There are two types of variations:

1. Direct proportion

2. Indirect or inverse proportion

Direct Proportion:

Two quantities a and b are said to be in direct proportion if-

•increase in a increases the b

•decrease in a decreases the b

For Example- If the number of kg of apples will increase then the cost will also increase and if the number of kg of apples will decrease then the cost will also decrease. So here, these two quantities (apple and its cost) are in direct proportion.

If, a and b are in direct proportion then the ratio of a and b is constant i.e a/b = k (k is constant)

 Observe the following table:

Observe that as the weight of the rice increases, the cost also increases in such a manner that their ratio remains constant.

So when ‘a’ and ‘b’ are in direct proportion where a1 and b1 are the initial values of any two quantities that are directly proportional to each other and a2 and b2 are the final values of those quantities, we can write: a1/b1 = a2/b2

Inverse Proportion:

Two quantities a and b are said to be in Inverse proportion if-

•Increase in a decreases the b

•Decrease in a increases the b

For Example: If the number of people will increase then the number of slice of cake per person will decrease and if the number of people will decrease then the number of slice of cake per person will increase. So here, these two quantities (no. of person and number of slice of cake) are in inverse proportion.

If a and b are in inverse proportion then the product of a and b is constant i.e a×b = k (k is constant) 

Let us look at the following situation. 

Amita can go to her school in four different ways. She can walk, run, cycle, or go by car.

If she,

• Walks at a speed of 3 km/hr she reaches school in 54 minutes.

• Goes to school running at the speed of 6 km/hr she reaches her school in 27 minutes.

• Goes to school by cycling at a speed of 9 km/hr she reaches her school in 18 minutes.

• Goes by car at a speed of 45 kilometres per hour she reaches her school in 3.6 minutes.

Speed*Time	The Product
3*54	162
6*27	162
9*18	162
45*3.6	162

Observe that as the speed increases, the time taken by amrita decreases in such a manner that their product remains constant.

So when ‘a’ and ‘b’ are in inverse proportion where a1 and b1 are the initial values of any two quantities that are directly proportional to each other and a2 and b2 are the final values of those quantities, we can write: a1*b1 = a2*b2