# Ratio and Proportion Important Formulas

## 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.

दो मात्रा में एक और एक ही इकाइयों में ख का अनुपात हिस्सा है और हम के रूप में एक यह रचना a: b

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

अनुपात एक में: b, हम प्राचार्य पद या पूर्ववर्ती और बी, दूसरे कार्यकाल या बाद के रूप में एक कहते हैं।

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.

दो अनुपात की निष्पक्षता अनुपात कहा जाता है। b = c: d को हम रचना एकa: b : c :: d और हम कहते हैं कि ए, बी, सी, डी अनुपात में होते हैं कि घटना एक में।

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 (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

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