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# When two quantities x and y are in ______ proportion or vary ______ they are written as x ∝ 1/y

**Solution:**

When x ∝ 1/y., it implies that x and y vary inversely as depicted by the table below:

x |
2 |
3 |
4 |
6 |
8 |

y |
24 |
16 |
12 |
8 |
6 |

As x increases y is decreasing.

x ∝ 1/ y

x = k/y

k = xy

k = 2 × 24 = 3 × 16 = 4 × 12 = 6 × 8 = 8 × 6 = 48

Hence we conclude that x and y are varying inversely. In other words they are in inverse proportion.

**✦ Try This: **From the data in the table below find the value of xy and conclude about the relationship between variables x and y.

x |
0.001 |
0.01 |
0.02 |
0.04 |
0.05 |

y |
1000 |
100 |
50 |
25 |
20 |

xy = 0.001 × 1000 = 0.01 × 100 = 0.02 × 50 = 0.04 × 25 = 0.05 × 20 = 1

Since xy = 1 and constant for all values of variable x and y it can be easily concluded that x and y are inversely related or in inverse proportion.

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

**NCERT Exemplar Class 8 Maths Chapter 10 Problem 20**

## When two quantities x and y are in ______ proportion or vary ______ they are written as x ∝ 1/y

**Summary:**

When two quantities x and y are in __inverse__ proportion or vary __inversely__ they are written as x ∝ 1/y

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