Ratio, Proportion & Variation Formula - 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
• Ifa<b,then a + x/b + x > a/b
• Ifa>b,then a − x/b − x > a/b
• If a<b,then a − x/b -x <a/b

4. Ifa/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
• Ifa<b,then a+x/b+x >a/b
• Ifa>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.

8. 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 a^1/3 : b^1/3

Product of proportions
1. 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:

1. 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.

2. If A and B are in a business for the same time, then Profit distribution ∝ investment (Time is constant).
3. If A and B are in a business with the same investment, then Profit distribution of investment ∝ Time (Investment is constant).
4. Profit Distribution ∝ investment
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.