Ratio and Proportion Exam Preparation

Author: mathqa22 | Posted: 20.07.2012

Ratio: Ratio means the number of times one quantity contains another quantity of the same kind. The comparison is made by considering what part or multiply the first quantity of the second. In a simple words the ratio gives a relation between two quantities. The ratio of two quantities a and b in the same units, is the fraction a/b and we write it as a:b.In the ratio a:b,we call a as the first term or antecedent and b, the second term or consequent. Ex: The ratio 3:7represents 3/7 with antecedent=3 and consequent=7.Rule:The multiplication or division of each term of the ratio by the same non-zero number does not affect the ratio.        

Proportion: The equality of two ratios is called proportion, that means if the two ratios are equal, then they make a proportion. If a:b=c:d,we write, a:b::c:d and we say a, b, c, d are in proportion. Here a and d are called extremes, while b and care called mean terms.                                                                                                      

Product of means=product of extremes

Types of Ratios and Proportions

Types Of Ratios:

Ratios are classified in to six types: 

1)Duplicate ratio: The ratio of the squares of the two numbers. Ex: 9:16 is the duplicate ratio of 3:4.                                

2)Triplicate ratio: The ratio of the cubes of the two numbers. Ex: 27:64 is the triplicate ratio of 3:4.                           

3)Sub-duplicate ratio: The ratio between square root of the two numbers. Ex: 4:5 is the sub-duplicate ratio of 16:25.          

4)Sub-triplicate ratio: The ratio between the cube roots of the two numbers. Ex: 4:5 is the sub-triplicate of 64:125.              

5)Inverse ratio: If the two terms in the ratio interchange their places, then the new ratio is inverse ratio of the first. Ex: 9:5  is the inverse ratio of 5:9.                                                                                                 

6)Compound ratio: The ratio of the product of the first term to that of the second term of two or more ratios. Ex: 3/4,5/7,4/5 and 3/5 is 3/4 x 5/7 x 4/5 x 3/5 = 9/35.

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Types Of Proportions:

1)Continued proportion: In the proportion 8/12=12/18, 8,12,18 are in the continued proportion.                                           

2)Fourth proportion: If a:b=c:x,then x is called forth proportion of a,b and c. The fourth proportion of a,b.c =bc/a                    

3)Third proportion: If a:b=b:x,then x is called third proportion of a and b. Third proportion of a,b =b^2/a                                

4)Second or mean proportion: If a:x=x:b,then x is called second or mean proportion of a and b. Therefore mean  proportion of a and b =Root of(ab)

Sample Examples on Ratio and Proportion for Exam Preparations

Example1:Find out the two quantities whose difference is 30 and the ratio between them is 5/11.?                              

Answer:

The difference of quantities, which are in the ratio 5:11,is 6.

To make the difference 30,we should multiply then  by 5.                          

Therefore 5:11=5x5:11x5=25:55.

Example2:What should be subtract from 15,28,20 and 38 so that the remaining numbers may be proportional?             

Answer:  If x is subtracted then,                                                                             

(15-x)/(28-x)=(20-x)/(38-x)                                                                     

(15-x)(38-x)=(28-x)(20-x)                                                                      

x^2-53x+570=x^2-48x+560                                                                

x^2-x^2-53x+48x=560-570                                                                                          

5x=10                                                                                                   

x=2

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