BOAT :

b ---> Boat speed/Man speed in water.

c ---> Current Speed/Speed of the River.

d ---> Down stream speed.

u ---> Up stream speed.

D ---> Total distance travelled.

T ---> Total time.

1.
d=b+c

2.
u=b-c

3.
b=(d+u)/2

4.
c=(d-u)/2

5.Average Speed=(2xy)/x+y      i.e

(b2-c2)/b

6.
D=[T(xy)]/x+y=[T(b2-c2)]/2b

7.
T=(D*2b)/b2-c2

8.
T=(D/d)+(D/u)=[D/(b+c)]+[D/(b-c)]

Formulae on Stock & Shares:-

1.No: of stock =
Total Stock/100
 Purchase Cost / (Mk.Vl + BR)

Sale Realisation / (Mk.Vl - BR)

Annual Income/Rate%

Formulae on Debentures:-

2.No: of Share =

Investment (or) Purchase Cost/[MK.VL(1 + B%)]

Sale Realisation/[Mk.Vl(1 - B%)]

(Annual Income * 100)/(Divident% * Face value)

CALENDERS

1. 100 years contains '5' odd days.

200 years contains '3' odd days.
300 years contains '1' odd days.
400 years contains '0' odd days.
2. Sunday -------> '0' odd day.
Monday -------> '1' odd day.
. .
. .
. .

3.One leap year contains '2' odd days.

4.The years which are mul of '4' are called leap years.

5.Leap year -------> 366 days (feb --> 29 days).

Ordinary year -------> 365 days.

6. MONTHS DAYS
Jan 31
Feb 28 (or) 29
Mar 31
Apr 30
May 31
Jun 30
Jul 31
Aug 31
Sep 30
Nov 30
Dec 31

7.One week = '7' days.

8.Leap year ------> '52' weeks + '2' odd days.

Ordinary year ------> '52' weeks + '1' odd day.
 BANKERS DISCOUNT
B.D -----------> Bankers Discount

S.I -----------> Simple Interest

T.D -----------> True Discount

B.G -----------> Bankers Gain

1.On bill for unexpired time ,

 B.D = S.I

2.
B.G = B.D - T.D

3.
B.G = S.I on T.D

4.
T.D = (P.W) * (B.G)

5.
B.g = (T.D)2/(P.W)

6.
B.D = (A * R * T)/100

7.
T.D = (A * R * T)/[100 + (R * T)]

8.
A = (B.D * T.D)/(B.D - T.D)

9.
T.D = (B.G * 100)/(R * T)

10.
Sum due = (B.D * T.D)/(B.D - T.D) = (B.D * T.D)/B.G Sum due =
Amount

11.
T.D/B.G = Sum/B.D

12.
B.D - T.D = A * {(R + T)2/[100(100 + (R * T))]}
 TRUE DISCOUNTS

T.D -----------> True Discount

P.W -----------> Present Worth

S.I -----------> Simple Interest

A -----------> Amount

R -----------> Rate

T -----------> Time

1.
A = P.W + T.D

2.
P.W = (100 * amount)/[100 + (R *
T)]
3.
T.D = (P.W * R *
T)/100

4.
T.D = (A * R * T)/[100(R +
T)]

5.
S.I on T.D = S.I - T.D

6.
sum = (S.I * T.D)/(S.I - T.D)

7.When the sum is put at C.I ,

P.W = A/[1 + (R/100)]T

8.
T.D = S.I on P.W

9.
P.W = (100 * T.D)/(R * T)

10.
T = (100 * T.D)/(P.W * R)

11.When the interest is at C.I ,

T.D = P.W[1+ (r/100)]t - P.W

 CLOCKS
workers
1.For coinciding the hands , workers

(5x) * (12/11)
x -----> first given time.workers

2.Right angles at each other , workers

(5x  15) * (12/11)

3.Opposite Direction ,
(5x - 30) * (12/11)

4.For finding time when it is 't'min space apart ,

(5x t) * (12/11)

5.For finding the angle between the hands of a clock is ,

30 * [HRS - (MIN/5)] + (MIN/2)

workers
 NUMBER SERIES
1.The difference between the no: and the no: obtained by interchanging the digits is 'x'.The
difference between digits is ,

diff = x/9

2.The sum of the no: and the no: obtained by interchanging the digits is 'y'.The sum of the
digits is ,

sum = y/11

3.The sum of two numbers is 'x' and their difference is 'y'.The product of the no: is ,

[(x + y)2 - (x - y)2]/4

4.
Dividend = (Divisor * Quotient) + Remainder

PIPES AND CISTERNS

1.
t (A + B) = (tA * tB)/(tA + tB)

2.
tA = (tB * t (A + B))/(tB - t (A + B))

3.Time for filling , (Filling pipe is bigger in size.)

F = (e * f)/(e - f)

4.Time for emptying , (emptying pipe is bigger in size.)

E = (f * e)/(f - e)

5.
T(A + B + C)=L/[(L/tA) + (L/tB) + (L/tC)]

6.Pipes 'A' & 'B' can fill a tank in f1hrs & f2hrs respectively.Another pipe 'C' can
empty the full tank in 'e'hrs.If the three pipes are opened simultaneously then the tank is
filled in ,

F = L/[(L/f1) + (L/f2) - (L/e)]

7.Two taps 'A' & 'B' can fill a tank in 't1' & 't2' hrs respectively.Another pipe 'C' can
empty the full tank in 'e'hrs.If the tank is full & all the three pipes are opened
simultaneously . Then the tank will be emptied in,

E = L/[(L/e) - (L/f1) - (L/f2)]

8.A filling tap can fill a tank in 'f'hrs.But it takes 'e'hrs longer due to a leak at the
bottom.The leak will empty the full tank in ,

E = [t(f * e) * tf]/[t(f + e) - tf]

9.Capacity of the tank is ,

F = (f * e)/(e - f)

10.
tc = [t(A + B) * t(A + B + C)]/[t(A + B) - t(A + B + C)]
11.
T = (xyz)/[(xz) + (yz) - (xy)]

MENSURATIONS

1. Square:-figure

(1)Area = a2Sq units.

(or)
 P2/16

(2)Perimeter = P =4a

(or)

a = P/4

(3)Digonal

(or)length of the rod that can be placed=

a = P/4

2.Rectangle:-figure

(1)Area =

l*b

(2)Perimeter = P =

2(l+b)

(3)Digonal =

d = l2+b2

b = d2-l2
l = d2-b2
3.If area of plot is given as 'z'm2
and the
ratio of l:b is given as x:y, then length is

l = x * [z/(x*y)]

b = y * [z/(x*y)]

4.

length required=(length * breadth of a room)/width of the carpet

5.

No:of stones =(length * breadth of a room)/(length * breadth of a stone)

6.

A2/A1= (a2/a1)2 = (d2/d1)2

7.

P2/P1=A2/A1
8.Circle:-figure

(1)Area =

r2 (or) (d2/4)

(2)

d = 2r

(3)Perimeter (or) Circumference =

2r = d

Where  = 22/7 (or) 3.14

(4)

A = c2/(4 ) (or) c = 4 A = 2A

9. % dec in Area =

fs [(r12 - r22)/r12] * 100

10. Distance travelled in 'N' revolutions is,

 D = N * d (or) N = D/(d)

11.Area left ungrazed =

a2(1 - /4)

12.Road out of the garden:-figure

(1)Area of the road =

2w[l+b+2w] = [(l+2w)(b+2w)]-(l*b)

Road inside the garden:-figure

(2)Area of the road =

2w[(l+b)-2w]

Two parallel roads:-figure

(3)Area of the road =

w[(l+b)-w]
13.Traingles:-

(1)Right angled traingles:-figure

Area = (1/2)*b*h

d = b2+h2

(2)Equilateral traingles:-figure
Area=

(3/4)a2

Perimeter = P =

3a

Height=

(3/2)a

(3)Scalene traingle:-figure

Perimeter = P =

2s=a+b+c

s=(a+b+c)/2
 Area =

s(s-a)(s-b(s-c)

(4)Isosceles traingle:-figure
Perimeter = P

2a+b

Area =

b/4(4a2-b2)

14.Volumes:-
(a)Cube:-figure
(1)Lateral surface area =

4a2

(2)Total surface area =

6a2

(3)Volume of a solid = Base area * Height =

 a 2 * a = a3

(4)Diagonal (or) Longest pole = d =

3a

(b)Cuboid:-figure

(1)Lateral surface area = AL =

2h[l+b]

(2)Total surface area = AT

2[lb+lh+bh]

(3)Volume = V =

lbh

(4)Diagonal = d =
 l2+b2+h2

(5)No:of boxes =

(lbh)/l1b1h1 = (Volume of big box)/(Volume of small box)

15.

a3 = v13+v23+v33

16.

a1/a2 = (v1/v2)1/3

17.No:of boxes(if areas are given) =

a3/a13 = (a/a1)3

(18)Cylinder:-figure

(1)Lateral surface area = AL =

2rh
 (2)Total surface area = AT

2r(h+r)

(3)

AT/Al=(h+r)/h

(4)Volume = v =

r2h

(5)Area of each flat surface i.e of ends =

r2

(19)Cone:-figure
(1)Slant height = L =

h2+r2

(2)Volume of the cone =

1/3(r2h)

(3)Curved surface area of cone =

rl
 (4)Total surface area =

r(l+r)

(5)

v1/v2=(r1/r2)2 * h1/h2

20.

H-h = (4/3) * rs 3/rd2

21.Area of circle inscribed in an equilateral

traingle is r2.It's height is,

h = 3r

(22)Sector:-figure
(1)

l= (/360)*2r

(2)A =

(/360)*r2
 (3)Circumference,c =

l+2r

(23)Four circular carboard pieces,each of radius 'r'cm

are placed in such a way that each piece touches two
other pieces.The area of the space enclosed by four
pieces is,

(2r)2 [1-/4]cm2

(24)Rhombus:-figure
(1)

4a2 = d12 + d22

(2)Area =

(1/2)d1d2

(3)Perimeter = P =

4a

(25)Parallelogram:-figure

(1)Area of leABC
 1/2(bh)

(2)Area of leACD

1/2(b/h)

(3)Area of parallelogram =

bh

(26)Trapezium:-figure

(1)Area of Trapezium=Area of (leABC + leACD)

1/2(ah) + 1/2(bh) = [(1/2)h][a + b]

(27)Sphere:-figure
(1)Surface area =

4r2

(2)Volume =
 4/3(r3)

(3)

A1/A2 = (r1/r2)2

(4)

v1/v2 = (r1/r2)3

(5)

v1/v2 = (A1/A2)3/2

(6)

A1/A2 = (v1/v2)2/3

28.Area of four walls =

2 * (length + breadth) * height

PROFIT AND LOSS

1.
Profit = S.P - C.P

2.
Loss = C.P - S.P

3.
Gain% = (Gain/C.P)*100

4.
Loss% = (Loss/C.P)*100

5.
S.P = [(100+Gain%)/100]*C.P

6.
C.P=S.P*[100/(100+Gain%)]

7.
S.P= [(100-Loss%)/100]*C.P

8.
C.P= S.P*[100/(100-Loss%)]

9.By selling an article for Rs/ '-S'1 , a man looses 'L%'.In order to gain 'G%' he uses the
following formula,

S1/(100-L%)=S2(100-G%)

10.If C.P of 'x' articies is equal to the S.P of 'y' articles,the profit% is:

[(x-y)/y]*100

11.
Gain%=[Error/(truevalue-error)]*100

12.
C.P = S.P/(1-losspart)

13.
C.P=S.P*[100/(100+g1)]*[100/(100+g2)]*[100/(100+g3]
14.
S.P=C.P*[(100+g1)/100]*[(100+g2)/100]*[(100+g3)/100]

15.
C.P = [(S.P1-S.P2)/x2-x1]*100

x1 ---------> gain1 (or) loss1

x2 ---------> gain2 (or) loss2

16.
S.P=C.P + [(C.P*g)/100]

17.Overall gain or loss =

(x1*g1)-(x2*L1)+(x3*g3)

Where x1,x2,x3 ----------> Parts of items sold

AGES
No seperate formulas,But problems are done by logical method.

Each part = Total Age/Sum of ratio's of Age's

 RATIO AND PROPORTION
1.If a:b = c:d , then Product of Means=Product of Extremes i.e

2ndterm*3rdterm=1stterm*4thterm

2.Each part =
Total Amount/Total of Ratios

3.If a:b = x:y & b:c = p:q ,then

a:b:c = xp:yp:yq

4.Third proportion to 'x' & 'y' =

y2/x

5.The mean proportion between 'a' & 'b' =

ab
 SIMPLIFICATIONS

1.
V ---> - (Veruculum)

B ---> () (Bracket)

O ---> of (of)

D ---> % (division)

M ---> * (Multiplication)

A ---> + (Addition)

S ---> - (Subtraction)

In this chapter, we must simplify the problems in

the above order only.
 DECIMAL FRACTIONS

1.

[ (a2-b2)/(a+b) ] = [ a-b ]

2.

[ (a2-b2)/(a-b) ] = [ a+b ]

3.

[ (a3+b3)/(a2-(a*b)+b2) ] = [ a+b ]

4.
 [ (a3-b3)/(a2-(a*b)+b2) ] = [ a-b ]

5.

[ (a+b)2+(a-b)2 /(a2+b2) ] = 2

6.

[ (a2+b2-(2*a*b) )/(a-b) ] = [ a-b ]

7.

[ (a2+b2+(2*a*b) )/(a+b) ] = [ a+b ]

L.C.M AND H.C.F
1.H.C.F of fractions =

[ H.C.F of Numerators/L.C.M of Denominators ]

2.    (i)which will be divided - L.C.M

      (ii)Which divides - H.C.F

3.The greatest number which can divide x, y and z leaving the same     remainder
'A' in each case is X-A = ?, Y-A = ?, Z-A = ? and Find     the H.C.F of obtained
numbers.

4.The greatest number by which if x and y are divided. The     remainder will be
A&B respectives is, x.A = ? , y-B = ? Find the     H.C.F of obtained numbers.

5.L.C.M of fractions =

[ L.C.M of Numerators/H.C.F of Denominators ]

6.
[ H.C.F * L.C.M = n1 * n2 ]

7. The least number which when divided by x,y and z leaves the      remainder A,B and C
respectively is, x-A = ? , y-B = ? , z-C = ?.      Here, there will be equal difference between
them i.e., D.

Required no = [ L.C.M of x,y and z ] - D

8.The smallest number which when diminished by A, is divisible by      p,q,r,s is,

Smallest no = [ (L.C.M of p,q,r,s) + A ]

ALLIGATION AND MIXTURES
1.

C.P = [ S.P/(100+g) *
100 ]

2.Mean rate of interest,

R = [ (100*I)/P*T) ]

3.Final % of Alcohol =

[ (Qi/Pi)/(Qi+Qw added) ]

Pi -----> Initial percentage

Qw -----> Quantity of water added

4.Final % of alcohol =

[ (Qi*Pi)/(Qi-Qw evoparated) ]

Qw -----> Quantity of water evoparated.

5.Quantity of water to be added =

[ Qmix * [(P2-P1)/(100-P2) ] ]
 P1 and P2 are percentages of water.

6.Other than water =

[ Qmix * (P1-P2)/P2 ]

P1 and P2 are the % of constituent other than

water (i.e., salt,alcohol etc)

7.Ratio of water to milk =

g/100

8. Percentage of water =

[
(100*g)/(100+g) ]

9.

[ 1- (y/x) ]n * x
 x -----> Capacity of container (or) Initial
quatity of pure milk.

y -----> Quantity drawn out each time.

n -----> No.of operations.

10.No.of rabits (4 legs) =

[ No.of legs given - (No.of heads given

* 2) ]/2

No.of pigeons =

[ No.of heads given - No.of

rabits ]

11. The mixture drawn out and replaced with water, so that the mixture
may be       half water and milk is =

[ (1/2) * (difference in parts/greater

part) ]

12.One gallon =

[ 100 litres ]
 TIME AND WORK
1.
tA+B = (tA * tB)/tA

2.
tB = (tA * tA+B)/tA - (tA+B)

3.
tA+B+C =[ L/(L/tA) + (L/tB) + (L/tC) ]

L ---> L.C.M of tA,tB,tC.

4.
tC =[ L/(L/tA+B+C) - (L/tB) - tB) ]
5.If A+B, B+C, A+C are given then A+B+C=?

   (i)
tA+B+C = 2L/[ (L/tA+B) + (L/tB+C) + (L/tC+A) ]

   (ii)
tC = 2L/[ (L/tB+C) + (L/tC+A) + (L/tA+B) ]

   (iii)
tB = 2L/[ (L/tA+B) + (L/tB+C) + (L/tA+C) ]

6.
S1d1 = S2d2

7.
wA+B = [ (wA * wB)/(wA+wB) ]

8.Working alternatively,

2 * tA+B = 2 * [ (tA.tB)/(tA+tB) ]
 COMPOUND INTEREST
1.
A=P[1+[
R/(100*n) n*t] ]

P -----> Principle

R -----> Rate % per annum

n -----> No.of convertions per year

T -----> Time in years

2.C.I=A-P      i.e.,

[ P [ 1+(R/(100*n)n*t]
-1]

3.When interest is calculated anually n=1,

A = P[1+
 (R/100)t]

4.When time is in fraction, t = x * (1/y) year:

A = P[1+(R/100)x] + [1 +
(1/y)*R/100 ]

5.When rate od interest is R1% R2%  R3% for Ist

year,IIndyear,
rd
III year respectively then amount,

A = P [ 1 + (R1100) * [1+(R2/100)]
[1+(R3/100)]

6.When difference between C.I and S.I on certain sum at

rate% on Rs.x,

[ C.I - S.I = sum *

(r/100)2 ]

i.e., [ D = P *
 (r/100)2 ]

Note: Applicable only for two years.

7.

D =[ (P*R2)
(300+R)/1003 ]

Note:Applicable only for 3 years.

8.

[ C.I/(200+R) =
S.I/200 ]

Note: Applicable only for 2 years.

9.

R = [ (2*difference of C.I and

S.I)/S.I ] * 100

10.R% amounts after 2 successive years we given:-

 R = [ (An+1-An)/An ] *
100

An+1 -----> Amount after (n+1) years.

An -----> Amount after (n+1) years.

11.

P =[ A32/A6 ] =
[ A22/A4 ] =
[ A12/A2 ] =
[A42/A8 ]

Note: Double the years.

12.

P =[ A23/A32 ] =
[ A34/A43 ] =
[ A45/A54 ]

Note: Consecutive years.

P =[A23/A6 ] =
[ A13/A3 ] =
[ A33/A9 ]
 13.

R =[( A6/A3)1/3 - 1 ] =
[ ( A4/A2 )1/2 - 1 ] =
[ ( A5/A2 )1/3 - 1 ]

R =[( A7/A2)1/3 - 1 ] =
[ ( A10/A2 )1/8 - 1 ] =
[ ( A10/A7 )1/3 - 1 ]

14.Installment problems:

a [ 100/(100+R) + 100/(100+R)2 +
100/(100+r)3 + ....... ] = B

a -----> Annual installment

B -----> Borrowed amount.

15.
R = [ (A/P)1/T - 1 ] *
100

16.
P = [ A2 *
[100/(100+R)]2 ]
AVERAGES
1.

Average = [ Total of observations/No.of observations ]

2.(i)When a person joins a group in case of increasing average Age         weight of new
comer  =

[ (Previous Age + No.of persons) * Increase in Avg ]

   (ii)In case of decreasing Average, Age (or) weight of new comer  =

[ (Previous Age - No.of persons) * Decrease in Avg ]

3.When a persom leaves a group and another person joins the group in the     place of
person left, then

   (i)In case of increasing average, Age (or) weight of new comer  =

[ (Age of person left + No.of persons) * Increase in Avg ]

   (ii)In case of decreasing Average, Age (or) weight of new comer  =

[ (Age of person left - No.of persons) * Decrease in Avg ]

4.When a person leaves the group but no body joins this group, then

   (i)In the case of increasing Average, Age (or) weight of man left  =

[ (Previous Age - No.of present persons) * Increase in Avg ]

   (ii)In case of decreasing Average, Age (or) weight of new comer  =

[ (Previous Age + No.of present persons) * Decrease in Avg ]

5.If a person travels a distance at a speed of x Km/hr returns to the original    place of y
Km/hr then average speed is

[ 2.x.y/(x+y) ]

6.If half of the journey is travelled at speed of x km/hr and the next half at a    speed of x
km/hr. Then average speed during the whole journey is

[ 2.x.y/(x+y) ]

7.If a person travels 3 equal distances at a speed of x Km/hr,

   y Km/hr,z km/hr.Then average speed during whole journey is

[ 3.x.y/(x.y+y.x+z.x) ]

8.
A
[ 3.x.y/(2x*y) ]

9.A

[ 3*L/[ (L/S1)+(L/S2)+(L/S3) ]

10.A

4L/[ (L.S1)+(L/S2)+L/S3)+(L/S4) ]

11.A
 1/[ (x/100) * (1/S1) ] + [y/100) * (1/S2) ] + [ (z/100)*(1/S3) ]

DISCOUNTS
1.
[Gain = x-d-
(x*d/100)]

x -----> Extra percentage added to C.P to

fix
M.P

d -----> Discount offered on M.P

g -----> Gain% obtained

2.
[Discount = M.P-
S.P]

3.
[d% = [ (M.P-S.P)/100] *
 100 ]

4.
[Discount = M.P * (d
%/100)]

5.Successive Discounts,

[ D = (d1+d2)-
(d1.d2)/100]

6.
[ (C.P/M.P) =
(100-d)/(100+g)]

7.
[M.P=(S.P2-S.P1)/(d2-d1) *
100]

8.
[S.P=M.P * (100-
d)/100]

9.
[S.P = M.P * [ (100-d1)/100 ] * [ (100-
d2)/100 ] ]

10.Difference of discounts =
[M.P * [ d1.d2/(100*100)
]]

11.
[ [ (100-d1)/(100-d2) ] =
 [ (100+g1)/(100+g2) ] ]

12.
Number of shirts = [ Total Discount/Discount
on each shirt ]

13.
[g% = [ (S.P-C.P)/C.P * 100 ] =
[ (gain/C.P) * 100 ] ]

14.
[C.P = (g/g%) *
100 ]

15.
[S.P = (g/g%) *
(100+g) ]

16.
[C.P = [S.P/(100+g)] *
100 ]

17.
[M.P = [C.P/(100-d)] *
100 ]

18.
G = [ (G1+G2)+
(G1.G2)/100]

19.
[(100-d)(100+g * M.P ] = [S.P *
(100)2]
 
[(S.P/M.P) = [ (100-d) * (100+g)
]/(100)2 ]
 SIMPLE INTEREST

1.

S.I = PTR/100

P -----> Principal

T -----> Time (in yrs)

R -----> Rate % per anum

2.
Amount = P+S.I

3.TO find the rate of interest per annum when a sum double/triple etc itself in x
years.Then,
[R * T = 100 * (n-1)]

4.
[(R1*T1)/R2*T2) = (N1-1)/(N2-1)]

5.
[(A/S.I = (100/R*T)+1]

6.
[R(or)T = (100*S.I)/P]

7.
[(R1-R2) = (More interest * 100/(P*t))]
 8.
A=[(P+S.I) = P(1+(T.R/100))]

9.
[P=(A1*T2-A2*T1)/T2-T1]

A ---> Amount

T ---> Time

10.
R=[(A2-A1)/(A1*T2-A2*T1)] * 100

11.
[I = ATR/(100+TR)]

12.If    I1= I2,

[(P1/P2) = (T2.R2)/T1.R1]

13.
[P = (100/Id)/(Rd.T)]

14.
[T = (100.Id/Pd.R)]

15.
[T = (100.Id/P R.d)]

16.
[R = (100.Is/Td.P)]

17.
[Gain = P.Rd.T/100]
 18.
[R = (100.ITotal)/(P1.T1+P2.T2+P3.T3)........]

19.
[P=(100.ITotal/(R1.T1+R2.T2+R3.T3+......)]

20.
a[ [100/100] + [(100+R)/100] + (100+2R)/100] + .......] = 0

a ---> Annual instalment.

D ---> Amount due

21.
A = P * [ (100+R1+R2+R3)/100]

PARTNERSHIP
1.Part of A/Part of B =

[(Amount invested by A*No.of months invested)/(Amount

invested by B*No.of months invested)]

2.Each part =

(Total profit/Total of Ratios)

CHAIN RULE

1.
M1D1T1S1W2 A2F2 = M2D2T2 S2W1A1F1

M -----> Men/labour

D -----> Days

T -----> Time (in hrs)

S -----> Speed

W -----> part of work done/wages

A -----> Amount earned

F -----> Food consumed/Milk used/coal required for

Machines/Diesel required for pumps.

2.D1W1 = D2W2
i.e.,
 D1(L2B2H2) =
D2(L1B1H1)

D ---> Days

L ---> Length

B ---> Broad (or) Breadth

H ---> Deep

3.Additional Men = M2-M1

PERCENTAGES
1. If x% is deducted on tax and y% of the remaining is spent on education and still there
is    a balance, the formula is :-

Balance * [ 100/(100-x) ] * [ 100/(100-y) ] * [ 100/(100-z) ]

2. The population of a town is 'P'. It increased by x% during I st year, increased

by y%    during IIst and again increased by z% during Ist. The population after 3
years will be,

P * [ (100+x)/100 ] * [ (100+y)/y ] * [ (100+z)/100 ]

3. % of effect
(i) Inc of x% Dec of x% x-y-[(x*y)/100]
(ii) Inc of x% Inc of y% (x+y)+[(x*y)/100]
(iii) Dec of x% Inc of y% [-x2/100]
(iv) Dec of x% Dec of y% (-x-y)+[(x*y)/100]
2
(v) Inc of x% Dec of x% [-x /100]
(vi) Inc of x% Inc of x% 2*x+[x 2/100]

4. (i) If the sides of the traingle,rectangle,square,circle,rhombus etc is increased by x%.Its

area is increased by
 2x+(x2/100)

   (ii)If decreased x%.Its ares is decreased by,

-2x+(x2/100)

5. In an examination x% failed in Hindi and y% failed in Science, if z% of the candidates

failed in both of the subjects. The percentage of students who passed in both of the
subjects is,

100-(x+y-z)

6. If A's income is r% more than B's income, the B's income is less than A's income by

(r/100+r) * 100%

7.If A's income is r% less than B's income, then B's income is more than A's income by

(r/100-r) * 100

8. (i)If the price of comodity increases by r% then reduction in consumption so as not to

increase the expenditure is

(r/100+r) * 100

   (ii)If the price of comodity decreases by r% then,

(r/100-r)*100

9.If the population of town (or) length of a tree is 'p' and its annual increase is r% then,

    (i)populaton (or) length of a tree after 'n' years is,

p[1+(r/100)]

   (ii)population (or) length of a tree 'n' years ago is,

p/[1+(r/100)n]
10.If the population of town (or) value of a machine is 'p' and annual decrease is r% then,
    (i)populaton (or) value of machine after 'n' years is,

p[1-(r/100)n]

   (ii)population (or) value of a machine 'n' years ago is,

p/[1-(r/100)n]

11.If 'A' is x% of 'C' and 'B' is y% of 'C' then 'A' is

(x/y) * 100%

   of 'B'.

12. If two values are respectively x% and y% more than a third value, then the first is

[(100+x) / (100+y)] * 100%

   of second

13.Total no.of votes  =

(Difference in votes/Difference in %) *
100

14.Maximum marks  =

[(pass marks/pass %) * 100]

15.Total marks  =

(Difference in marks / Difference in

%)*100
16. (i)Reduced rate  =

[(Amount/Quantity more) * (Reduction % /100)]

     (ii)Original rate (or) previous rate  =

[(Amount/Quantity more) * (Reduction % /100-

reduction%)]

17. (i)Increased rate  =

[(Amount/Quantity less) * (increase % /100)]

     (ii)Original rate (or) previous rate  =

[(Amount/Quantity less) * (Increase % /100-increase

%)]

18. If the numeratorof fraction is increased by x% and its denominator is

diminished by       y% ,the value of the fraction is A/B.Then the original
fraction is,

(A/B) * [(100-y) / (100+x)]