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Chapter 03 : Ratio and Proportion > Ratio
Ratio and proportion is the continuation of the basic concepts for the entrance tests. The application of the topics is far and wide, a direct application which will be covered here is “Allegation and Mixtures”.
The comparison of two quantities of the same unit is the ratio of one quantity to another. The ratio of A and B is written as A: B or A / B, where A is called the antecedent and B the consequent.
Example: The ratio of 10 kg to 20 kg is 10:20 or 10/20, which is 1:2 or ½, where 1 is called the antecedent and 2 the consequent.
Properties of Ratio
1. a : b = ma : mb, where m is a constant
2. a : b : c = A : B : C is equivalent to a / A = b /B = c /C, this is an important property and has to be used in ratio of three things.
3. If a / b = c / d , then
(a+b) / b=(c+d) / d – Componendo
Example: ½ = 2/4, so (1+2)/2 = (2+4)/4 => 3/2 = 6/4 => 3/2 = 3/2
(a-b) / b = (c-d) / d – Dividendo
Example: 10/4 = 20/8, so (10-4)/4 = (20-8)/8 => 6/4 = 12/8 => 3/2 = 3/2
(a+b) / (a-b) = (c+d) / (c-d) – Componendo and Dividendo
Example: 10/4 = 20/8, so (10+4)/(10-4) = (20+8)/(20-8) => 14/6 = 28/12 => 7/3 = 7/3
Application: These properties have to be used
with quick mental calculations; one has to see a ratio and quickly
get to results with mental calculations.
Example: 10/4 = 20/8, should quickly tell us that 14/4(7/2) = 28/8(7/2), 6/4(3/2) = 12/8(3/2) and 14/6(7/3) = 28/12(7/3)
4. If a / b = c / d =e / f = ……, then (a+c+e+…..)/(b+d+f+….)
= each of the individual ratio
Example: ½ = 2/4 = 4/8, there fore (1+2+4)/(2+4+8) = 7/14 = ½
5. If A > B then (A+C)/ (B+C) < A/B Where A, B and C are natural numbers
Example: 3>2, then (3+4)/ (2+4) = 7/6 (1.16)
6. If A < B then (A+C)/ (B+C) > A/B Where
A, B and C are natural numbers.
Other topics covered
Basic Arithmetic Operations
Properties of Numbers
Profit and Loss
Simple and Compound Interest
Time, Speed and Distance
Work and Time
Indices and Surds
Permutations and Combinations