APTITUDE

Numbers
H.C.F and L.C.M
Decimal Fractions
Simplification
Square and Cube roots
Average
Problems on Numbers
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Surds and Indices
Percentage
Profit and Loss
Ratio And Proportions
Partnership
Chain Rule
Time and Work
Pipes and Cisterns
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Trains
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Alligation or Mixture
Simple Interest
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Logorithms
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Races and Games of Skill
Calendar
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True Discount
Bankers Discount
Oddmanout and Series
Data Interpretation
probability
Permutations and Combinations
Puzzles
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RATIO AND PROPORTION
Important Facts: 1.Ratio : The ratio of two qualities 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 of antecedent and b, the second term consequent. Ex: The ratio 5:9 represents 5/9 with antecedent=5 ,consequent=9 3Rule: The multiplication or division of each term of 9 ratio by the same non-zero number does not affect the ratio. 4.Proportion: The equality of two ratios is called proportion. If a:b=c:d, we write a:b::c:d and we say that a,b,c and d are in proportion. Here a and b are called extremes, while b and c are called mean terms. Product of means=product of extremes Thus, a:b::c:d => (b*c)=(a*d) 5.Fourth proportional: If a:b::c:d, then d is called the fourth proportional to a,b and c. 6.Third proportional: If a:b::b:c, then c is called third proportional to a and b. 7.Mean proportional: Mean proportional between a and b is SQRT(a*b). COMPARISION OF RATIOS: We say that (a:b)>(c:d) => (a/b)>(c/d) 8.Compounded ratio: The compounded ratio of the ratios (a:b), (c:d),(e:f) is (ace:bdf). 9.Duplicate Ratio: If (a:b) is (a2: b2 ) 10.Sub-duplicate ratio of (a:b) is (SQRT(a):SQRT(b)) 11.Triplicate ratio of (a:b) is (a3: b3 ) 12.Sub-triplicate ratio of (a:b) is (a1/3: b1/3 ). 13.If a/b=c/d, then (a+b)/(a-b)=(c+d)/(c-d) (componend o and dividend o) VARIATION: 14.we say that x is directly proportional to y, if x=ky for some constant k and we write. 15.We say that x is inversely proportional to y, if xy=k for some constant and we write. 16. X is inversely proportional to y. If a/b=c/d=e/f=g/h=k then k=(a+c+e+g)/(b+d+f+h) If a1/b1,a2/b2, a3/b3..............an/bn are unequal fractions then the ratio. a1+a2+a3+..........an/(b1+b2+b3+...............bn) lies between the lowest & the highest of the three fractions.
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