Triplicate Ratio

Introduction

The triplicate ratio is a compound ratio that is used in mathematics to solve the cube of two quantities. In this study, the meaning of the triplicate ratio will be explained. Various triplicate ratio examples will be elaborated. By the end of this guide, the method of subtriplicate ratio will be analyzed.

What is a Triplicate Ratio?

Ratio defines a comparative relation between the same types of two quantities in an equal unit. A Triplicate ratio can be defined as a ratio that holds the value of multiplication of three equivalent ratios. This implies that three identical ratios are multiplied to produce the resulting ratio, which is known as Triplicate Ratio. The Triplicate Ratio consists of three equivalent ratios m: n, m: n, and m: n that is (m)3: (n)3. This ratio can be further categorized as the Sub Triplicate ratio. Therefore, it could be said that this ratio is a compound ratio of three identical ratios. 

In other words, 

The triplicate ratio of p: q = Compound ratio of p; q, p; q, and p; q 

That is, (p * p * P): (q * q * q) 

Or, (p)3: (q)3

The above representation is the formula to calculate a triplicate ratio. 

Triplicate Ratio Examples in Mathematics 

The examples of triplicate ratio are defined below:

Example 1: 

For finding out the triplicate ratio of 5: 8

Solution, 

= (5 * 5 * 5): (8 * 8 * 8)

= (5) 3: (8)3

= 125: 512 

Therefore, the solution to the problem is 125: 512. 

From the above example, it can be seen that the triplicate ratio gives the cube root of the quantities as its resulting ratio. 

Example 2:

For Finding out the Triplicate ratio of 25: 27,

Solution, 

= (25 * 25 * 25): (27 * 27 * 27)

= (25)3: (27)3

= 15625: 19683 

Hence, the result is 15625: 19683. 

Example 3: 

If (2a + 3): (5a + 4) is a triplicate ratio of 3: 4, then for finding out the square of a,

Solution, 

Given,

(2a + 3): (5a + 4) is a triplicate ratio of 3: 4.

Concept used,

The triplicate ratio of m: n i.e., m 3: n3. 

Calculation,

The triplicate ratio of 3: 4 = (3) 3: (4) 3 

= 27: 64

As per the given question, 

= > (2a + 3): (5a + 4) = 27 / 64 

= > 64 (2a + 3) = 27 (5a + 4) 

= > 128a + 192 = 135a + 108

= > 192 – 108 = 135a – 128a

= > 84 = 7a

= > 84 / 7 = a

= > 12 = a

i.e., a = 12

Therefore, the square of a that is, 12 is = 144.

How to find Sub Triplicate Ratio?

Like the triplicate ratio, there is the existence of a subtriplicate ratio as well. A subtriplicate ratio can be defined as the ratio, which gives the cube roots of two quantities. The formula used to calculate the subtriplicate ratio of two quantities is given below:

The subtriplicate ratio of m: n is, 

3 √ m: 3 √ n 

For example 1, finding out the subtriplicate ratio of 27: 1,

As it is known, that cube root of 27 is 3 and the cube root of 1 is 1. Hence, 

= 3 √ 27: 3 √ 1

= 3: 1

The result gives the ratio is 3: 1. 

The other example to illustrate the subtriplicate ratio, 

Example 2: What is the subtriplicate ratio of the following quantities (i) 343: 729, (ii) 3375: 8000. 

Solution (i),

Given, 

343: 729

Concept used,

The subtriplicate ratio of c: d is = 3-√ c: 3 √ d

Calculation, 

3 √343: 3 √ 729

= 7: 9

Therefore, the subtriplicate ratio of 343: 729 is 7: 9.

Solution (ii),

Given, 

3375: 8000

Concept used,

The sub triplicate ratio of c: d i.e., 3 √c: 3 √ d

Calculation, 

 3 √ 3375: 3 √ 8000

= 15: 20 

Therefore, this gives the result of the subtriplicate ratio of 3375: 8000 is 15: 20.

Conclusion

After the above discussion, it can be concluded that the application of the triplicate ratio has been used to solve various mathematical approaches. This is one of the simplest parts of mathematics in order to solve proportion-related problems. The formula of subtriplicate ratio is another useful approach to find out the ratio of cube roots of two or more quantities. In this study, various triplicate ratio examples and the subtriplicate ratios have been discussed which could help to understand this topic immensely.