Sub duplicate ratio

There are many concepts in ratios. The ratios concept is little difficult because there are many formulae and concepts to remember. This sub duplicate ratio concept is one among them.

Now before getting into the concept of sub duplicate ratio or before going deep into sub duplicate ratio, let us now see what is meant by duplicate ratio.

Duplicate ratio:

Duplicate ratio can be defined as when two types of equal ratios are multiplied, then it is called duplicate ratio.

For example, the duplicate ratio of s/t is  s2/t2

The duplicate ratio can also be defined on other terms

The compound ratio of two same ratios is also called as duplicate ratio.

It can be written as s:t and s:t which gives  s2:t2.

Now we can clearly understand the concept sub duplicate ratio.

What is meant by sub-duplicate ratio?

Sub duplicate ratio can be defined as the square root of two or more ratios.

Sub duplicate ratio is the concept in duplicate ratio.

Sub duplicate ratio uses the concept of both duplicate ratio and compound ratio.

How to find sub duplicate ratio?

Sub duplicate ratio can be calculated based on the question they have given. If the question is given directly to find the sub duplicate ratio 

Formulae for sub duplicate ratio

As we told sub duplicate uses square root function. Sub duplicate can be solved by used square roots of the following terms. 

•                    a : b =a:b

Now let us look into some examples to clearly explain and understand what is meant by sub duplicate ratio.

Examples of sub duplicate ratio

Example 1

Find the sub duplicate ratio of 4:9?

Solution

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

Formula used:

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

Here in the above given problem, Let us consider the terms a as 4 and b as 9

The square root of 4 is 2

And the square root of 9 is 3.

Therefore, sub duplicate ratio of 4: 9 is 

• 4:√9
• 2:3

Hence the sub duplicate ratio of 4:9 is 2 :3.

Example 2

Find the sub duplicate ratio of 625:841?

Solution

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

Formula used:

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

Here in the above given problem, Let us consider the terms a as 625 and b as 841

The square root of 625 is 25

And the square root of 841 is 29.

Therefore, sub duplicate ratio of 625: 841 is 

• 625:√841
• 25:28

Hence the sub duplicate ratio of 625:841 is 25:28.

It is easy to find the square root and sub duplicate for composite numbers. Now let us take prime numbers and find the sub duplicate ratio for them.

Example 3

Find the sub duplicate ratio of 23:19?

Solution

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

Formula used:

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

Here in the above given problem, Let us consider the terms a as 23 and b as 19

Both 23 and 19 are prime numbers and their square root will be in decimal form.

The square root of 23 is 4.79

And the square root of 19 is 4.35.

Therefore, sub duplicate ratio of 23: 19 is 

• 23:√19
• 4.79:4.35

Hence the sub duplicate ratio of 23: 19 is 4.79:4.35.

So far now have seen with two terms

Now let us seem more than two terms,

• To find sub duplicate ratio we will use formula a: b =a:b
• To find sub duplicate ratio we will use formula a: b:c =a:b:√c
• To find sub duplicate ratio we will use formula a: b:c:d =a:b:c:√d:
• For multiple terms the sub duplicate ratio of a:b:c:d:…. Is a:b:c:d.

Example 3

Find the sub duplicate ratio of 1600:3600:6400?

Solution

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

Formula used:

To find sub duplicate ratio we will use formula a: b: c =a:b:√c

Here in the above given problem, Let us consider the terms a as 1600 and b as 3600 and c as 6400

The square root of 1600 is 40

And the square root of 3600 is 60.

And the square root of 6400 is 80.

Therefore, sub duplicate ratio of 1600:3600:6400 is 

• √1600:√3600:√6400
• 40:60:80
• 4:6:8
• 2:3:4

Hence the sub duplicate ratio of 1600:3600:6400 is 2:3:4.

Example 4

The sub duplicate ratio of 64:49 is 8:x, Find the term x?

Solution

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

Formula used:

To find sub duplicate 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 49 and a  is 8

The square root of 64 is 8

And the square root of 49 is 7.

Therefore, sub duplicate ratio of 64: 49 is

Conclusion

Sub duplicate ratio is the sub topic of duplicate ratio. Sub duplicate ratio can be defined as when there are two ratios or when there are two duplicate ratios and their square roots of their ratios is considered as the sub duplicate ratio. To find sub duplicate ratio we will use formula a: b =a:b. For multiple terms the sub duplicate ratio of a: b: c: d: …. Will be a:b:c:d……We are know that double means twice, so in sub duplicate topic we will perform square roots to the given problem. Sub duplicate ratio concept is one of easy concepts in ratios. 

• 64:√49
• 8:7

Hence the sub duplicate ratio of 64:49 is 8:7.

Therefore, x is 7