# If on increasing a, b decreases in such a manner that _______ remains ______ and positive, then a and b are said to vary inversely with each other.

**Solution:**

The following table shows the values of variable a and b.

a |
2 |
3 |
4 |
5 |
6 |

b |
3 |
2 |
3/2 |
6/5 |
1 |

The above table reveals that when x is increasing, y is decreasing. We need to establish proportionality between the two variables:

x ∝ 1/y

xy = k

xy = 2 × 3 = 3 × 2 = 4 × (3/2) = 5 × (6/5) = 6 × 1 = 6 = k

Hence x and y are inversely proportional.

**✦ Try This: **If on decreasing a, b increases in such a manner that _______ remains ______ and positive, then a and b are said to vary inversely with each other.

The following table shows the values of variable a and b.

a |
5/2 |
3/2 |
1/2 |
1/3 |
1/4 |

b |
2 |
10/3 |
10 |
15 |
20 |

The above table reveals that when x is increasing, y is decreasing. We need to establish proportionality between the two variables:

a ∝ 1/b

ab= k

ab = 5/2 × 2 = 3/2 × (10/3) = (1/2) × 10 = (1/3) ×15 = (1/4) × 20 = 5 = k

Hence a and b are inversely proportion

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

**NCERT Exemplar Class 8 Maths Chapter 10 Problem 30**

## If on increasing a, b decreases in such a manner that _______ remains ______ and positive, then a and b are said to vary inversely with each other.

**Summary: **

If on increasing a, b decreases in such a manner that __ab__ remains constant and positive, then a and b are said to vary inversely with each other.

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