Important Formula: Ratio & Proportion

# Important Formula: Ratio & Proportion | Quantitative Aptitude (Quant) - CAT PDF Download

Ratio and Proportions is one of the easiest concepts in CAT. It is just an extension of high school mathematics.

• Questions from this concept are mostly asked in conjunction with other concepts like similar triangles, mixtures and alligations.
• Hence fundamentals of this concept are important not just from a stand-alone perspective, but also to answer questions from other concept
1. Ratio is the comparison between similar types of quantities; it is an abstract quantity and does not have any units.
2. If a/b = c/d , then a, b, c, d are said to be in proportion.
3. If a/b = c/d, then
If a, b, x are positive, then
If a>b, then a+x/b+x <a/b
If a<b,then a+x/b+x >a/b
If a>b,then a−x/b−x >a/b
If a<b,then a−x/b-x<a/b
4. If a/p = b/q = c/r = d/s = ..., then a:b:c:d:...= p:q:r:s:...
(a) a × d = c × b

5. If a, b, x are positive, then
If a>b, then a+x/b+x < a/b
If a<b, then a+x/b+x > a/b
If a>b, then a−x/b−x > a/b
If a<b, then a−x/b-x < a/b
6. If a/p= b/q = c/r =d/s =...,then a:b:c:d:...=p:q:r:s:...

7. Types of ratios:
Duplicate Ratio of a:b is a2 :b2
Sub-duplicate ratio of a:b is Sqrt(a): Sqrt(b)
Triplicate Ratio of a:b is a3 :b3
Sub-triplicate ratio of a : b is a1/3 : b1/3

Product of proportions:

If a:b = c:d is a proportion, then

• Product of extremes = product of means i.e., ad = bc
• Denominator addition/subtraction: a:a+b = c:c+d and a:a-b = c:c-d
• a, b, c, d,.... are in continued proportion means, a:b = b:c = c:d = ....
• a:b = b:c then b is called mean proportional and b2 = ac
• The third proportional of two numbers, a and b, is c, such that, a:b = b:c ▪ d is fourth proportional to numbers a, b, c if a:b = c:d

Variations:

• If a ∝ b, provided c is constant and a ∝ c, provided b is constant, then a ∝ b x c, if all three of them are varying.
• If A and B are in a business for the same time, then Profit distribution ∝ Investment (Time is constant).
• If A and B are in a business with the same investment, then Profit distribution ∝ Time of investment (Investment is constant).
• Profit Distribution ∝ Investment × Time.

EduRev's Tip: If a/b = c/d = e/f = k

Given two variables x and y, y is (directly) proportional to x (x and y vary directly, or x and y are in direct variation) if there is a non-zero constant k such that y = kx. It is denoted by y ∝ x
Two variables are inversely proportional (or varying inversely, or in inverse variation, or in inverse proportion or reciprocal proportion) if there exists a nonzero constant k such that y = k/x.

The document Important Formula: Ratio & Proportion | Quantitative Aptitude (Quant) - CAT is a part of the CAT Course Quantitative Aptitude (Quant).
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## FAQs on Important Formula: Ratio & Proportion - Quantitative Aptitude (Quant) - CAT

 1. What is a ratio in mathematics and how is it used?
Ans. A ratio is a comparison of two or more quantities. It is represented as a fraction or using the colon symbol (:). Ratios are used to express the relationship between different quantities and are often used to solve problems involving proportionality.
 2. How do you simplify a ratio?
Ans. To simplify a ratio, you need to find the greatest common divisor (GCD) of the two numbers in the ratio and divide both numbers by it. By dividing both numbers in the ratio by their GCD, you can obtain the simplest form of the ratio.
 3. What is the difference between a direct proportion and an inverse proportion?
Ans. In a direct proportion, as one quantity increases, the other quantity also increases in the same ratio. For example, if the number of workers increases, the amount of work done also increases proportionally. In an inverse proportion, as one quantity increases, the other quantity decreases in the same ratio. For instance, if the speed of a car increases, the time taken to cover a certain distance decreases proportionally.
 4. How do you solve a proportion problem?
Ans. To solve a proportion problem, you need to set up an equation with two ratios or fractions. Cross-multiply the terms in the equation and then solve for the unknown variable. This method is called the cross-multiplication method and helps find the value of the unknown variable in the proportion.
 5. Can ratios and proportions be used in real-life situations?
Ans. Yes, ratios and proportions are used in various real-life situations. They are commonly used in cooking recipes to adjust ingredient quantities, in finance to calculate interest rates, in construction to determine scale drawings, and in medicine to calculate medication dosages based on the patient's weight. Understanding ratios and proportions is essential in solving problems that involve comparison and proportionality in real-life scenarios.

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