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# Two quantities are said to vary ______ with each other if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant

**Solution:**

Let us consider the table where the values of variables x and y are given:

x |
1 |
2 |
3 |
4 |
5 |

y |
3 |
6 |
9 |
12 |
15 |

In the above table as x is increasing y is also increasing.

Therefore:

x/y = 1/3 = 2/6 = 3/9 = 4/12 = 5/15 = 1/3 = k

Hence the ratio k remains constant. Therefore the relationship between x and y is direct.

Let us see the next table where the reverse is happening i.e.as x is decreasing y is also decreasing

x |
20 |
16 |
12 |
8 |
4 |

y |
10 |
8 |
6 |
4 |
2 |

Here x is decreasing and y is also decreasing

x/y = 20/10 = 16/8 = 12/6 = 8/4 = 4/2 = k = 2

The value of k is a constant. Hence there is a direct relation between the two variables.

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

p |
1 |
2 |
3 |
4 |
5 |

q |
7 |
14 |
21 |
28 |
35 |

p/q = 1/7 = 2/14 = 3/21 = 4/28 = 5/35 = 1/7 = k

Hence the value of k is 1/7

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

**NCERT Exemplar Class 8 Maths Chapter 10 Problem 23**

## Two quantities are said to vary ______ with each other if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant

**Summary:**

Two quantities are said to vary __directly__ with each other if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant

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