# Two quantities are said to vary ______ with each other if an increase in one causes a decrease in the other in such a manner that the product of their corresponding values remains constant

**Solution:**

Consider the following table where as x increases y decreases. The value of the xy is determined as follows.

x |
0.002 |
0.004 |
0.008 |
0.016 |
0.05 |

y |
500 |
250 |
125 |
62.5 |
31.25 |

To verify that relationship between x and y is inversely proportion the value of k has to be ascertained

xy = k

xy = 0.002 × 500 = 0.004 × 250 = 0.016 × 62.5 = 0.05 × 31.25 = 1 = k

Since k is a constant equal to 1 we can state that x and y are inversely proportional.

Let us take another example below:

x |
18 |
12 |
9 |
6 |
4 |

y |
2 |
3 |
4 |
6 |
9 |

To verify that relationship between x and y is inversely proportion the value of k has to be ascertained

xy = k

xy = 18 × 2 = 12 × 3 = 9 × 4 = 6 × 6 = 4 × 9 = 36 = k

Since k is a constant equal to 36, we can state that x and y are inversely proportional.

**✦ Try This: **What is the value of the constant of proportionality between the two variables p and q?

p |
42 |
28 |
21 |
14 |
12 |

q |
2 |
3 |
4 |
6 |
7 |

p/q = 42/2 ≠ 28/3 ≠ 21/4 ≠ 14/6 ≠ 12/7 ≠ k

pq = 42 × 2 = 28 × 3 = 21 × 4 = 14 × 6 = 12 × 7 = 84 = k

Hence variables p and q are inversely proportional.

**☛ Also Check: **NCERT Solutions for Class 8 Maths Chapter 13

**NCERT Exemplar Class 8 Maths Chapter 10 Problem 24**

## Two quantities are said to vary ______ with each other if an increase in one causes a decrease in the other in such a manner that the product of their corresponding values remains constant

**Summary:**

Two quantities are said to vary __inversely__ with each other if an increase in one causes a decrease in the other in such a manner that the product of their corresponding values remain constant

**☛ Related Questions:**

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