** Ratio:** Correlation of any two zodiac sign, from which it is realized that the second amount is the number of the first amount, the ratio is called. The ratio is expressed by the (:) sign, such as 5: 7 or 7 meters in ratio 5: 7 or ^{ 5}/_{7} .

Here the first post 5 of this ratio is called Antecedent and the second term 7 is called the final result

**Decrease or Reciprocal Ratio: **The proportion in which the second type of amount is decreased due to the increase of the first type.

**Compound Ratio: **The complex ratio of the ratio of two positions or two to two ratios and the ratio of the product of their final positions is said.

As-complex ratio of 2: 3, 4: 5 and 3: 5

= (2 × 4 × 3): (3 × 5 × 5) = 8: 25

** The quadratic ratio or the Duplicate Ratio: a: b: c is the quadratic ratio a ^{2} : b^{2} : c^{2 }**

** example – **What would be the quadratic ratio of 5: 7: 8?**
Solution – **The quadratic ratio of 5: 7: 8 = 5

**Triplet ratio or concentration ratio**: a: b: c concentration a^{3} : b^{3} : c^{3}.

** Example – **What happens in the concentration of 3: 5: 4?**
Solution – **3: 5: 4 concentration of

= 3

**TYPE-1 **

** Example -1. **If A: B = 4: 5 and B: C = 6: 7, then what will be the value of A: C?

**Example-2. **If the part of Part B of ^{ 2}/_{3} and part of c of ^{3}/_{4} , then what will be the value of A: C?

** Tricky Solution: **A: C = 2 × 3: 3 × 4 = 1: 2 **Answer.**

[^{A}/_{B} = ^{2}/_{3} ⇒ A:B = 2:3 Similarly, B: C = 3: 4]

** Example-3. **If A: B = 7: 9 and B: C = 3: 5, then what will be the value of A: B: C?**
Tricky Solution:** A: B: C = (7: 9) × 3: 9 × 5 = 21: 27: 45 = 7: 9: 15

**TYPE-2 **

** Example-1. **If A: B = 3: 4, B: C = 8: 9 and C: D = 12: 13, then what’s A: D equals?

**Example-2. **If the value of A is ^{ 2}/_{5} of part B of B The value of c ^{ 2}/_{3} of c and the value of C is equal to ^{ 1}/4 of D, So what will be the value of A: D?

** Tricky Solution: **A: D = 2 × 2 × 1: 5 × 3 × 4 = 1: 15

** Example-3. **If A: B = 4: 5, B: C = 3: 4 and C: D = 6: 7, then what will be the value of A: B: C: D?**
Tricky Solution: **A: B: C = (4: 5) × 3: 5 × 4 = 12: 15: 20

A: B: C: D = (12:15 to 20) × 6: 20 × 7 = 36: 45: 60: 70

**TYPE-3 **

** TRICK – **

**Proportion: **When two proportions are equal in number, then that expression is called proportionately.

**Eg**– a: b = c: d ⇒ a: b :: c: d

In this proportion, a, b, c and d are respectively called first, second, third, and fourth proportional. A and d are the external amounts and secondary and zerom are called b and c. Product of external amounts (a × d) = Product of secondary quantities (b × c)

** TYPE-4 **

**Continuous proportion: **The ratio of a and b to the number three, a and b, is equal to the ratio of b and c, then this expression is called continuous proportion. Such as: a: b = b: c ⇒ a: b:: b: c In the above expression, a, b and c are respectively called first, middle, and third proportion.

**TYPE-5**

**TYPE-6**

**TYPE-7**

**TYPE-8**

**TYPE-9**

Follow