The topic duplicate ratios are very common among the competitive exams. And every year you will find at least 2-3 questions from it. Besides the direct questions, ratio and proportion can also be important in percentage and decimals. Today we will be explaining you on the duplicate ratios. Questions from this are not very common but you may require this concept in other ratio and proportion questions.

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## Duplicate Ratios

In ratio and proportion, you do not need to remember any formulae to solve the questions. You just need to understand the concept and try and have more and more practice of the questions.

There are concepts you need to understand in duplicate ratios. One is duplicate ratios itself and the other is a sub-duplicate ratio. In duplicate ratios, when the ratio p/q is compounded with itself, the resulting ratio which is p²/q² is called as the duplicate ratio. For example, 16/9 is the duplicate ratio of 4/3.

The duplicate ratio of the ratio of a:b is also defined as the compound ratio of a:b and a:b

=> (a × a):(b × b) => a²:b²

So, the duplicate ratio of 6:7 = 6²:7² = 36:49

Similarly, for the sub-duplicate ratio, √a/√b is the sub-duplicate ratio of a/b or a:b. For example 3:4 is the sub-duplicate ratio of 9:16. There are other ratios as well as triplicate ratios and sub-triplicate ratio but we will go into it in the other article.

**Browse more Topics under Ratios And Proportions**

- Propotion Of Quantities
- Proportionals (Third, Fourth and Mean)
- Comparison of Ratios
- Invertendo, and Alternendo
- Componendo, and Dividendo
- Componendo-Dividendo
- Variations
- Ratios and Proportion Practice Questions

### Solved Example

Q. If there are 10 people that can clean 10 floors by 10 mops in 10 days, in how many days can 8 people clean 8 floors with 8 mops?

A. 12 1/2 days B. 8 days C. 10 days D. 12 days

There are direct questions of duplicate ratios but this is one of an example where you can use the concept of duplicate ratios to find the answer. Here you are required to find the man-days. So, you cannot directly find the answer.

Now, 10 men and 10 days mean 100 man-days are required to clean 10 floors with 10 mops. Thus, 1 floor requires 10 man-days to get cleaned. Hence, you can establish that to clean 8 floors you will require 80 man-days. Thus, 10 days are required to clean the 8 floors using 8 mops. So, the correct answer is C.

## Practice Questions

1. Find the ratio which is sub-duplicate of 64:81 and duplicate ratio of the ratio 4:5.

A. 4:3 B. 16:9 C. 5:4 D. 7:5

Ans. The correct answer is B.

2. Let’s suppose that every cow gives 7 liters of milk every week. How many cows are required to get 45 liters of milk in 15 days?

A. 2 cows B. 3 cows C. 4 cows D. None of the above

Ans. The correct answer is B.

3. Suppose that the duplicate ratio of a:b is (a – x):(b – x), then find the value of x

A. ab/a + b B. ab/a – b C. ab/a^2 – b D. None of the above

Ans. The correct answer is A.

4. Raj and Abhay consume calories in the ratio of 3:5 every day. Both of them does exercise and lose calories in the ratio 3:5. If Abhay absorbs 3500 calories every day, what are calories absorbed by Raj?

A. 2100 calories B. 2000 calories C. 1800 calories D. 1750 calories

Ans. The correct answer is A.