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# On increasing a, b increases in such a manner that a/b remains______ and positive, then a and b are said to vary directly with each other

**Solution:**

When a increases and b increases and a/b remains constant then we can write:

a ∝ b

a/b = k, where k = proportionality constant

Only when k is constant for various values of variables a and b, we can conclude that a and b are in direct proportion.

The table below reflects

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

b |
3 |
6 |
9 |
12 |
15 |

a/b = 1/3 = 2/6 = 3/9 = 4/12 = 5/15 = 1/3 = k

The constant k is 1/3 and a & b are said to vary directly with each other.

**✦ Try This: **On decreasing x, y decreases in such a manner that a/b remains______ and positive, then a and b are said to vary directly with each other.

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

y |
1/3 |
1/6 |
1/9 |
1/12 |
1/15 |

As we can see from the above table, as ‘x’ decreases, ‘y’ also decreases.

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

The constant k is 3 and hence x and y are said to be direct proportion

On decreasing x, y decreases in such a manner that a/b remains __constant__ and positive, then a and b are said to vary directly with each other.

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

**NCERT Exemplar Class 8 Maths Chapter 10 Problem 29**

## On increasing a, b increases in such a manner that a/b remains______ and positive, then a and b are said to vary directly with each other

**Summary:**

On increasing a, b increases in such a manner that a/b remains __constant__ and positive, then a and b are said to vary directly with each other

**☛ Related Questions:**

- If on increasing a, b decreases in such a manner that _______ remains ______ and positive, then a an . . . .
- If two quantities x and y vary directly with each other, then ______ of their corresponding values r . . . .
- If two quantities p and q vary inversely with each other then ______ of their corresponding values r . . . .

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