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You don’t need to recall any formulae to solve the ratio and proportion questions. All you have to do now is practise the questions as much as possible. When the ratio p/q is compounding in multiple ratios, the resultant ratio, p2/q2, is the duplicate ratio. The duplicate ratio of 4/3, for instance, is 16/9. The compound ratio of a:b and a:b is also known as the duplicate ratio of a :b proportion. => (a × a):(b × b) => a²:b²
So, the duplicate ratio of 6:7 = 6²:7² = 36:49
Solved Example
How many days does it take for eight individuals to clean eight floors utilising eight mops if ten people can clean ten floors with ten mops in ten days?
- 12 1/2 days B. 8 days C. 10 days D. 12 days
There are direct duplicate ratio issues, but here is one case in which the concept of duplicate ratios can be used to obtain the solution. You must identify the person-days in this section. As a result, you won’t discover the answer directly.
With ten workers and ten days, cleaning ten floors with ten mops will take 100 man-days. As a result, cleaning one level takes ten man-days. As a result, you may calculate that cleaning eight floors will take 80 man-days. As a result, cleaning the eight floors with eight mops will take ten days. As a result, C is the correct response.
Duplicate Ratio Questions
Every day, Priya and Abhay consume calories in a 3:5 ratio. Each of the exercises also burns calories at a 3:5 ratio. So what did Priya absorb the calories if Abhay consumes 3500 calories per day?
- 2100 calories B. 2000 calories C. 1800 calories D. 1750 calories
The correct answer is A.
Types of Ratio
There are several different forms of ratios:
Compounded Ratio: When we take the ratio of an antecedent as that of the combination of the ratios’ antecedents and the resultant ratio as the combination of the ratios’ consequent, we get a compounded ratio. The compound ratio of m: n and p: q, for instance, is mp: nq, while the ratio of a: b, c: d, but also e: f is ace: bdf.
Duplicate Ratio: The duplicate factor is the proportion of two ratios to the same. The duplicate ratio of a: b, for example, is a2 : b2. In other words, the duplicate ratio of the ratio a: b is equal to the compound ratio of a: b and a: b.
= (a × a) : (b × b)
= a2 : b2
The ratio of Equalities: The ratio is also called the ratio of equality if the antecedent and consequent are equal, such as 5: 5.
The ratio of Inequalities: The ratio is also called the inequality ratio when the antecedent and consequent are not equal, such as 5:7.
Conclusion
The proportion and ratio of squares are known as duplicate proportion and duplicate ratio. Thus, the first terms to the third seem to have been in a duplicate ratio of first to the second, and as its square would be to the square of the second in geometrical proportions. As a result, the ratio of 2 to 8 in 2, 4, 8, 16 is the same as the ratio of 2 to 4, or as the square of 2 would be to the square of 4. I hope now you understand all about duplicate ratios. By reading this information, you will clear all your doubts.
