The document Important Formula: Ratio & Proportion CAT Notes | EduRev is a part of the Quant Course Quantitative Aptitude (Quant).

All you need of Quant at this link: Quant

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

- Ratio is the comparison between similar types of quantities; it is an abstract quantity and does not have any units.
- If a/b = c/d , then a, b, c, d are said to be in proportion.
- 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 - If a/p = b/q = c/r = d/s = ..., then a:b:c:d:...= p:q:r:s:...

(a) a × d = c × b - 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 If a/p= b/q = c/r =d/s =...,then a:b:c:d:...=p:q:r:s:...

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:**

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.

Offer running on EduRev: __Apply code STAYHOME200__ to get INR 200 off on our premium plan EduRev Infinity!

116 videos|131 docs|131 tests