Ratio and Proportion – Important Formulas
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.
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.
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).
In the event that a : b = c : d, then d is known as the fourth proportion to a, b, c.
a : b = c : d, then c is known as the third proportion to an and b.
Mean proportion amongst an and b is √ab
4.Comparison of Ratios:
We say that
|(a : b) > (c : d)||a||>||c||.|
The Compound Ratio of the ratio: (a : b), (c : d), (e : f) is (pro : bdf).
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 (a1/3 : b1/3).
In the event that a =
|If||a||=||c||, then||a + b||=||c + d||. [componendo and dividendo]|
|b||d||a – b||c – d|
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
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