Triplicate ratio

Ratios include a wide range of subjects. The ratios concept is a little difficult to grasp because there are so many formulae and concepts to remember. The concept of a triplicate ratio is one of them.

Let’s define triplicate ratio first.

Triplicate ratio

Triplicate ratio can be defined as cubing of ratios. Or it can also be defined as compound ratio of three same ratios is called triplicate ratio.

It will be clearly understandable, when we go through examples.

Formula of triplicate ratio:

The triplicate ratio of m/n can be calculated by using formula  m3:n3 

Let us same three same terms as shown below as m: n, m: n, m: n

When we perform compound ratio, we will get m3:n3

Here, m3 is the antecedent and  n3 is the consequent.

Since, triple means three and so we cube the ratios rather than squaring the ratios.

Sub-Triplicate ratio:

Sub triplicate ratio is also one of the topics in ratios topic.

Sub triplicate ratio can be defined as cube rooting the ratios.

It can also be defined as cube root of compound ratio of three same terms is called sub triplicate ratio.

For example, the sub triplicate ratio of m:n is ∛m:∛n

How do we solve triplicate problems?

Triplicate problems are solved with the following step

We can use either formula m3:n3 or when terms of same ratios given, multiply all the antecedents thrice and multiply all the consequents thrice. The resultant antecedent: consequent will be the triplicate ratio of given problem.

Triplicate ratio can not only be done for two or three terms, it can be done for multiple numbers of terms.

Now lets us look into some example of triplicate ratio

Examples of triplicate ratio

Example 1

Find the sub triplicate ratio of 12:14?

Solution

Hint: Triplicate ratio can be calculated by using the concepts of ratios.

Formula used:

To find triplicate ratio we will use formula m: n =m3:n3

Here in the above given problem, Let us consider the terms m as 12 and n as 14

The cubing of 12 is 1728

And the cubing of 14 is 2744.

Therefore, triplicate ratio of 12: 14 is 

• 123:143

• 1728 : 2744

Hence the triplicate ratio of  123:143Is 1728 : 2744

Example 2

Find the triplicate ratio of 4:16?

Solution

Hint: Triplicate ratio can be calculated by using the concepts of ratios.

Formula used:

To find triplicate ratio we will use formula m: n =m3:n3

Here in the above given problem, Let us consider the terms a as 4 and b as 16

The cubing of 4 is 64

And the cubing 16 is 4096.

Therefore, triplicate ratio of 4:16 is 

• 43:163

• 64:4096

• 1:64

Hence the sub triplicate ratio of 43:163

 is 1: 64

Example 3

Find the sub triplicate ratio of 64:216?

Solution

Hint: Sub triplicate ratio can be calculated by using the concepts of ratios.

Formula used:

To find sub triplicate ratio we will use formula a: b =∛a:∛b

Here in the above given problem, Let us consider the terms a as 64 and b as 216

The cube root of 64 is 4

And the cube root of 216 is 6.

Therefore, sub triplicate ratio of 64: 216 is 

• ∛64:∛216

• 4:6

• 2:3

Hence the sub duplicate ratio of 64: 216 is 2: 3

Example 4

Find the sub triplicate ratio of 64:216 and triplicate ratio 5: 6 ?

Solution

Hint: Sub triplicate ratio can be calculated by using the concepts of ratios.

Formula used:

To find sub triplicate ratio we will use formula a: b =∛a:∛b

Here in the above given problem, Let us consider the terms a as 64 and b as 216

The cube root of 64 is 4

And the cube root of 216 is 6.

Therefore, sub triplicate ratio of 64: 216 is 

• ∛64:∛216

• 4:6

• 2:3

Hence the sub duplicate ratio of 64: 216 is 2: 3

To find triplicate ratio we will use formula m: n =m3:n3

Here in the above given problem, Let us consider the terms a as 5 and b as 6

The cubing of 5 is 125

And the cubing 6 is 216.

Therefore, triplicate ratio of 5:6 is 

• 53:63

• 125:216

Hence the duplicate ratio of 53:63 is 125:  216

Example 5

Find the triplicate ratio of 30:60?

Solution

Hint: Triplicate ratio can be calculated by using the concepts of ratios.

Formula used:

To find triplicate ratio we will use formula m: n =m3:n3

Here in the above given problem, Let us consider the terms a as 30 and b as 60

The cubing of 30 is 27000

And the cubing 60 is 216000.

Therefore, triplicate ratio of 30:60 is 

• 303:603

• 27000 :216000

• 27: 216

Hence the triplicate ratio of 43:163   is 27: 216

Now let us seem more than two terms,

• To find triplicate ratio we will use formula m: n = m3:n3

• To find triplicate ratio we will use formula m: n:s =m3:n3:s3

• To find triplicate ratio we will use formula m: n:s:t  =m3:n3:s3:t3

• For multiple terms the triplicate ratio of a: b: c: d:…. is m3:n3:s3:t3

Example 6

Find the triplicate ratio of 3:6:9?

Solution

Hint: Triplicate ratio can be calculated by using the concepts of ratios.

Formula used:

To find triplicate ratio we will use formula m: n: s =m3:n3:s3

Here in the above given problem, Let us consider the terms m as 3 and n as 6 and s as 9

The cubing of 3 is 27

And the cubing 6 is 216.

The cubing of 9 is 729

Therefore, triplicate ratio of 3:6:9 is 

• 33:63:93

• 27: 216: 729

Hence the triplicate ratio of 33:63:93   is 27: 216:729

Conclusion

Triplicate ratio can be defined as cubing of ratios. The main difference between triplicate and sub triplicate is in triplicate ratio, we perform cubing and at sub triplicate ratio, we will cube root the ratio.

For, prime numbers when we perform sub-triplicate ratio, we will get result in decimal form. And for composite numbers when we perform sub triplicate ratio we will get result in real numbers because we are performing cube root. But it is different while performing triplicate ratio, for both prime numbers and composite numbers the result will be in real numbers form.