# Ratio and Proportion Important Formulas

Maths Tricks 0 Comments## Ratio and Proportion – Important Formulas

**1. Ratio:**

The Ratio of two amounts an and b in the same units, is the part and we compose it as a : b.

In the Ratio a : b, we call an as the principal term or predecessor and b, the second term or subsequent.

Eg. The Ratio 5 : 9 represent 5/9 with predecessor = 5, resulting = 9.

Principle: The increase or division of every term of a proportion by the same non-zero number does not influence the Ratio.

Eg. 4 : 5 = 8 : 10 = 12 : 15. Additionally, 4 : 6 = 2 : 3.

**2.Proportion:**

The fairness of two Ratio is called proportion. In the event that a : b = c : d, we compose a : b :: c : d and we say that a, b, c, d are in proportion.

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Here an and d are called extremes, while b and c are called mean terms.

Result of means = Product of extremes.

In this manner, a : b :: c : d (b x c) = (a x d).

**3.Fourth Proportional:**

In the event that a : b = c : d, then d is known as the fourth proportion to a, b, c.

**Third Proportional:**

a : b = c : d, then c is known as the third proportion to an and b.

Mean Proportional:

Mean proportion amongst an and b is √ab

**4.Comparison of Ratios:**

We say that

(a : b) > (c : d) |
a |
> | c |
. |

b |
d |

**Compound Ratio:**

The Compound Ratio of the ratio: (a : b), (c : d), (e : f) is (pro : bdf).

**5.Duplicate Ratios:**

Duplicate Ratio of (a : b) is (a² : b²).

Sub-Duplicate Ratio of (a : b) is (a : b).

Triplicate ratio of (a : b) is (a³ : b³).

Sub-triplicate ratio of (*a* : *b*) is (*a*^{1/3} : *b*^{1/3}).

In the event that a =

If | a |
= | c |
, then | a + b |
= | c + d |
. [componendo and dividendo] |

b |
d |
a – b |
c – d |

**6.Variations:**

We say that x is specifically proportional to y, if x = ky for some steady k and we compose, x y.

We say that x is conversely proportional to y, if xy = k for some consistent k and

we compose,

x |
1 | . |

y |

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