ratio and proportion

comparison of two quantities in terms of how man times is called ratio

 

ex: lets decide 100 to 2 persons 1:1 ratio

100/2= 50 each

6:8:10 = 24 aboe

1:3 water to squash

Simple Ratio: lowest 

 

15:35 = 3:7 (5) 3+7=10 ( 1% of 10 = 1 )

inverse ratio / reciprocal ratio

ex a:b=b:a

A income 2x than b

2A=1B
A/B=1/2 1:2

 

Equivalent ratio: ratios are obtained by multiplying or dividing by any counting number are equivalent ratios.

Ratio is comparison between quantities in same measures or units

Duplicate Ratio of a:b = a 2^:b2 (superscript)

 

20000  by a:b:c 3:4:5 duplicate ratio

duplicate ratio means square 9:16:25

9+16+25=50  total ratio

20000/50= 400

1=400

400*9=3600

400*16= 6400

400*25=10000  (total 20K)

 

SUb DUplicate ratio : square root  sQuare root of 400 = 20

Triplicate Ratio: Menas 3x than current ratio   Qube a3

3:4 = 27:64

sub triplicate ratio: root qube

ex: 216:343:729 = 6:7:9

Compound Ratio: 

2:3 & 5:2 = (2*5=10) (2*3=6)

10:6=5:3 (divided by 2)

 

 

a:b = 4:5

b:c = 5:7

abc = 4:5:7

 

2nd ex:

a:b= 4:5

b:c=10:9

abc = ?

(4:5)2= 8:10

8:10:9

3rd ex

a:b= 2:3

b:c= 3:4

c:d =6:7

abcd = ?

A	B	C	D
2:	3	3	3
3	3:	4	4
6	6	6:	7

step 1: same values occupied left or right

Step 2 divide by 2 & 3 to get lowest values.

ratio:

6:9:12:14

 

2nd ex Multiplication

a:b = 3:5

b:c = 7:4

d:c (inverse ratio) = 2:3

A	B	C	D
3:	5	5	5
7	7:	4	4
3	3	3:	2

 

Bold marks are originals

step 1: add same values left or right for occupy

step 2: multiply  if divide not possible

7*3=21=3 63,  5*7=35*3=105,  (5*4=20*3=60) (5*4=20*2=40)

63:105:60:40

 

 

Proportion 

 

a:b::c:d  or a/b=c/d