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Concept of Inverse Proportion

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Two quantities may change in such a manner that if one quantity increases, the other quantity decreases and vice versa. 
For example, as the number of workers increases, time taken to finish the job decreases. Similarly, if we increase the speed, the time taken to cover a given distance decreases. To understand this, let us look into the following situation. 
Zaheeda can go to her school in four different ways. She can walk, run, cycle or go by car. Study the following table. 

Observe that as the speed increases, time taken to cover the same distance decreases. 
As Zaheeda doubles her speed by running, time reduces to half. As she increases her speed to three times by cycling, time decreases to one third. Similarly, as she increases her speed to 15 times, time decreases to one fifteenth. (Or, in other words the ratio by which time decreases is inverse of the ratio by which the corresponding speed increases). 

Note : Multiplicative inverse of a number is its reciprocal. Thus, `1/2` is the inverse of 2 and vice versa. Note that `2 xx 1/2 = 1/2 xx 2 = 1`
Thus two quantities x and y are said to vary in inverse proportion, if there exists a relation of the type xy = k between them, k being a constant. 
If `y_1, y_2` are the values of y corresponding to the values `x_1, x_2` of x respectively then `x_1y_1 = x_2y_2 (= k),` or `x_1/x_2 = y_2/y_1`
We say that x and y are in inverse proportion.

Let us consider some examples where we use the concept of inverse proportion.
When two quantities x and y are in direct proportion (or vary directly) they are also written as x ∝ y.
When two quantities x and y are in inverse proportion (or vary inversely) they are also written as `x ∝ 1/y`

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