Quant formulae and shortcuts for Bank PO and SSC
Quant formulae and shortcuts for Bank PO and SSC
Here we are presenting some most important Quant formulae and shortcuts for Bank PO and SSC. This quant cheat sheet can be very handy for the last minute revision before the exam.
 HCF & LCM
LCM × HCF = Product of the Numbers
 Algebra
 a^{2} – b^{2} = (a – b)(a + b)
 (a+b)^{2} = a^{2} + 2ab + b^{2}
 a^{2} + b^{2} = (a – b)^{2} + 2ab
 (a – b)^{2} = a^{2} – 2ab + b^{2}
 (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2ac + 2bc
 (a – b – c)^{2} = a^{2} + b^{2} + c^{2} – 2ab – 2ac + 2bc
 (a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3} ; (a + b)^{3} = a^{3} + b^{3} + 3ab(a + b)
 (a – b)^{3} = a^{3} – 3a^{2}b + 3ab^{2} – b^{3}
 a^{3} – b^{3} = (a – b)(a^{2} + ab + b^{2})
 a^{3} + b^{3} = (a + b)(a^{2} – ab + b^{2})
 (a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}
 (a – b)^{3} = a^{3} – 3a^{2}b + 3ab^{2} – b^{3}
 (a + b)^{4} = a^{4} + 4a^{3}b + 6a^{2}b^{2} + 4ab^{3} + b^{4})
 (a – b)^{4} = a^{4} – 4a^{3}b + 6a^{2}b^{2} – 4ab^{3} + b^{4})
 a^{4} – b^{4} = (a – b)(a + b)(a^{2} + b^{2})
 (a + b + c)^{3} = a^{3} + b^{3} + c^{3} + 3(b+c)(c+a)(a+b)
 a^{3} + b^{3} + c^{3 }3abc = (a+b+c) (a^{2} + b^{2} + c^{2} – ab – bc – ca)
 If (a+b+c) = 0, a^{3} + b^{3} + c^{3 }= 3abc
 Surds and Indices
 (a^{m})(a^{n}) = a^{m+n}
 (ab)^{m}= a^{m}b^{m}
 (a^{m})^{n}= a^{mn}
 a^{0}= 1
 (a^{m})/(a^{n}) = (a^{mn})
 (a^{m}) = 1/ (a^{m})
 Progressions:
In an Arithmetic progression (AP) with first term and common difference ,
 Nth term of AP =
 Sum of n terms of AP =
In a Geometric Progression (GP) with first term and common ratio ,
 Nth term of GP =
 Sum of n terms of GP =
 For an infinite GP where , sum of the series is
Harmonic Progression: A series in which reciprocal terms are in AP. Harmonic mean of two numbers and is given by
 Percentages
 Effective percentage of x% and y% = . If there is a percentage decrease, the value is used with a negative sign.
 Profit & Loss

Simple & Compound Interest
Watch Trick on Simple & Compound Interest
 Alligations and Mixtures
Direct formula for removal and replacement in mixtures:
‘x’ amount of milk is there in the vessel and ‘a’ is taken out and replaced with water. If the process is repeated ‘n’ times, then the quantity of milk remaining in the vessel =
 Time Speed Distance
 Distance = Speed x Time
 Average speed =
 Speed conversion from km/hr to m/s
 Speed conversion from m/s to km/hr
 If the ratio of the speeds of A and B is a : b, then the ratio of the times taken by them to cover the same distance is
 If a man covers a certain distance at x km/hr and an equal distance at y km/hr. Then, the
 If two persons A and B start at the same time in opposite direction from two points and after passing each other, they complete the journey in ‘a’ and ‘b’ hrs respectively, then
 A Man covers a certain distance at x km/h and gets late/early by ‘a’ minutes. When he travels at y km/h, he reaches ‘b’ minutes late/early. Distance travelled in this case is given by
[Difference of time should be taken by accounting late and early in the problem]
 If the speed of boat in still water is ‘u’ km/h and speed of the stream is ‘v’ km/h, then
 Downstream speed = (u+v) km/h
 Upstream speed = (uv) km/hr
 If the speed downstream is ‘a’ km/hr and speed upstream is ‘b’ km/hr, then
 Speed of boat in still water = km/h
 Speed of stream = km/h
 Time & Work, Wages, pipes & Cisterns
 If A can do a piece of work in p days and B can do the same in q days, A and B together can finish it in [pq / (p+q)] days
 MDH formula: where M= no. of men, D= no. of days, H= no. of hours per day and W= amount of work.
 Permutations/Combinations
 Number of permutations of ‘n’ things, taken ‘r’ at a time is given by:
 Number of combinations of ‘n’ things, taken ‘r’ at a time is given by:
 If there are ‘n’ objects, out of which ‘p’ are alike of one kind, ‘q’ are alike of second kind, ‘r’ are alike of third kind, and remaining all are different, then permutations is given by
 Circular permutations: the number of circular permutations of n different things taken all at a time is given by (n1)!, if clockwise and anticlockwise orders are taken as different.
 In case of a garland or necklace, no. of circular permutations become x (n1)! , as clockwise and anticlockwise arrangements are treated as same.
 Probability
Probability means chance of occurrence of an event. In its basic form, probability is calculated as:
Probability =
Eg. If two coins are tossed, probability of both heads is 1/4. This is because the total cases are (HH),(HT),(TH),(TT) out of which favourable cases is only (HH).
All the exam questions can be solved by just remembering this formula. You can log on to www.examformula.com to better understand the concept and exam problems.
Quant formulae and shortcuts for Bank PO and SSC
 Trigonometry
Pythagoras Theorem: , where ‘a’ and ‘b’ are perpendicular and base and c is the hypotenuse
Trigonometry Identities:
Formulas involving cofunction identities:
sin(90−x)=cosx
cos(90−x)=sinx
tan(90−x)=cotx
cot(90−x)=tanx
Sum/ difference formulas:
Double Angle Formulas:
Formulas involving Product Identities:
Formulas for Sum to Product Identities:
 Mensuration
2D FIGURES:
Rectangle:
 Area = length x breadth
 Perimeter = 2 × (Length + Breadth)
 Length of the Diagonal =
Square:
 Area =
 Perimeter =
 Length of Diagonal =
Parallelogram:
 Area =
 Perimeter = 2 × (Length + Breadth)
Triangle:
 Area =
Area (using heron’s formula) = ; where s (semiperimeter) =
where a,b,c are sides of the triangle
 Area of equilateral triangle =
Trapezium:
 Area =
 Area =
 Perimeter =
Circle:
 Area =
 Circumference =
 Area of sector =
 Length of an arc =
3D FIGURES:
Cuboid:
 Volume =
 Total surface Area =
 Length of diagonal =
Cube:
 Volume =
 Total surface area =
 Length of leading diagonal =
Cylinder:
 Volume =
 Curved Surface Area =
 Total Surface Area =
Cone:
 Volume =
 Curved surface Area =
 Total Surface Area =
 Slant Height =
Sphere:
 Volume =
 Surface Area =
Hemisphere:
 Volume =
 Curved Surface Area =
 Total Surface Area =
Prism:
 Volume =
 Lateral Surface Area =
 Total Surface Area =
Pyramid:
 Volume =
 Total Surface Area =
 Linear & Quadratic Equations
 Roots of equations are:
 is called the Discriminant (denoted by ‘D’). The value of D tells about the nature of roots of the equation:
 If D>0, the equation has two real and distinct roots
 If D=0, the equation has two real and equal roots
 If D<0, the equation has no real roots
 Sum of roots = , product of roots =
 Coordinate Geometry
 Distance Formula: Distance between two points (x_{1,} ,y_{1}) and (x_{2} ,y_{2}) is given by:
 Section Formula: The point which divides the line joining two points (x_{1,} ,y_{1}) and (x_{2} ,y_{2}) internally is:
The point which divides the line joining two points (x1, ,y1) and (x2 ,y2) externally is:
 Mid point:
 Slope of a line:
 Angle between two lines: For two lines, y1=m1x1+c1 and y2=m2x2+c2 which make angles , the slopes are given by
Angle between the lines is:
Watch Video on Coordinate Geometry
 Simplification
 BODMAS Rule: The rule says that you have to solve any mathematical expression in correct sequence. The sequence of BODMAS is as follows:
B = Bracket
O = Order (Powers, Square Roots, etc.)
DM = Division and Multiplication (lefttoright)
AS = Addition and Subtraction (lefttoright)
If some formulae are left, we will cover it in the upcoming articles. Hope you enjoyed this compilation. Stay tuned for more and share with your friends!