Ratios and proportions

Ratios and proportions is one of the most important topic in aptitude because of wide range of it's applications like ages, percentages, mixtures and allegations...
Ratio is a quantitative relation between two or more numbers which tells how many times one number is w.r.t other.

If a certain amount N is divided among A, B in a ratio a:b then
A's share is a/(a+b) * N and B's share is b/(a+b) *N
If A:B = a:b and B:C = c:d then A:C = a*c : b*d
If A:B = p:q, B:C = r:s, C:D = t:u then
A:D = A/D = (A/B) * (B/C) * (C/D)  
If a quantity is increased by a/b then the new content becomes (a+b)/b
If a quantity is decreased by a/b then the new content becomes (b-a)/b

To reduce your computations, it is always recommended to remember these values in terms of percentages
1/1 = 100 %
1/2 = 50 %
1/3 = 33.33 %

1/4 = 25 %
1/5 = 20 %

1/6 = 16.66 %
1/7 = 14.28 %       1/13 = 7.6%
1/8 = 12.25 %       1/12 = 8.33%
1/9 = 11.11 %       1/11 = 9.09%
1/10 = 10 %
Proportion is a number considered in comparative relation to a whole
when 3 numbers are given a, b, c and asked to find the fourth proportion (x) then a/b = c/x
Mean proportion of two numbers a,b is x then x^2 = a*b
If A=B*C then B, C are Inversely proportional and A,B or A,C are directly proportional
 If A is kept constant, Increase in B should reflect decrease in A and vise versa
If B is kept constant, Increase in one term should reflect increase in another term.

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Sample Questions:
Question 1:
If a sum of 600 rupees is divided among A and B in a ratio 2:3 then what is the difference between their shares.
Solution:
Difference = (3/5 - 2/5 )*600 = 120

A's share = 2/5 (600) = 240
B's share = 3/5 (600) =  360 or 600-240
difference = 360-240 = 120.

Question 2:
If A:B = 5:3 and B:C = 6:7, find A:B:C
Solution:
A:B = (5 : 3)*6  B:C = (6 : 7)*3
A:B:C = 30 : 18: 21

Question 3:
If A:B = 2:3, B:C = 3:4 and C:D=8:9,  find A:D
Solution:
A:D = (A/B)(B/C)(C/D)
        = (2/3)(3/4)(8/9)
        = 4/9

Question 4:
Find the Fourth proportion (x) of 2,5,12
Solution:
2/5 = 12/x
x=6/5

Question 5:
Find the mean proportion of 625,900
Solution:
x^2 = 25^2 * 30^^2
x=25*30
x = 750

Many tricks on the way, stay tuned :)