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#### Exercise 11.2 class 8 solution-inverse proportion

Inverse proportion, also known as inverse variation, is a mathematical relationship between two variables in which an increase in one variable results in a decrease in the other variable and vice versa. In simple terms, when one variable goes up, the other goes down, and vice versa, and this relationship can be described using an equation of the form:

xy=k

Where:

- x and y are the two variables.
- k is a constant of proportionality.

In an inversely proportional relationship, as one variable increases, the other variable decreases in such a way that their product remains constant. This means that the product of x and y will always be the same value, k, no matter the values of $x$ and $y$.

**For example**, if you’re driving at a constant speed, the time it takes to reach a certain destination is inversely proportional to your speed. If you double your speed, you’ll reach the destination in half the time because the product of speed and time remains constant. Mathematically, this can be expressed as:

$\text{Speed\xc3\u2014Time=Constant}$

Two quantities (variables) are said to be in inverse proportion if increase in one quantity leads to decrease in other quantity in same ratio or vice-versa. For example,

(i) If the number of workers increases, time taken to finish the same work decreases.

(ii) if the speed of a vehicle increases, the time taken to cover the same distance decreases.

#### Exercise 11.2 class 8 solution- Examples of inverse proportion

Let us consider an example. A school wants to spend 6000 on mathematics books. If the rate of one book is 40, then how many books could be bought? Clearly 150 books can be bought.

If the price of book is more than 40, then the number of books which could be purchased with the same amount of money will be less than 150. Observe the following table.

if we double the price of book i.e 40*2=80,the number of books that can be purchased by same amount will be 150*1/2=75 (i.e halved). if we increase the price by three times i.e 40*3=120 ,the no. of book can be purchased with same amount will be 150 * 1/3 = 50 i.e one third.

we observe that price of book increases and number of books purchased by same amount decreases.

Note: The product of the corresponding values of two quantities is fixed constant i.e. 40 * 150 = 80 * 75 = 120 * 50 = 200 * 30 = 6000

If we represent the price of one book as x and number of books purchased as y, then as x increases, y decreases in same ratio and vice versa.It is important to note that the product xy remains fixed constant.

Note: So two quantities x and y are said to vary inversely, If there exist a relation of the type xy=k, between them,where k is constant.

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#### Exercise 11.2 class 8 solution- solution pdf

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