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...